text: You will ﬁrst need to determine the order of the resulting matrix. MINVERSE function results in the #N/A error in extra cells selected, The MINVERSE function must be entered as the. A Matrix for which you want to compute the inverse needs to be a square matrix. The way to check it is to multiply matrix A and A-1 . First you need some data. Step 4: Enter the range of the array or matrix, as shown in the screenshot. We also can check whether the inverse we get through the MINVERSE function is correctly captured or not. the matrix B = 2 −4 −3 6 has no inverse since det(B) = 0, you make get something that looks like this: 2. Again, to create a matrix you select all the members of a matrix. The MINVERSE function returns the inverse (opposite) matrix of an array. It is mandatory to select all the cells where your inverse will be computed. Inverse Matrix: The reciprocal of a number is called the “inverse matrix”. Here we discuss How to create Inverse Matrix in Excel along with practical examples and downloadable excel template. If there is any blank cell or non-numeric value in a given matrix, MINVERSE will give you #VALUE! Let’s take the matrices from up above and find the product using matrix multiplication in Excel with the MMULT function: First, let’s find C, the product of AB. MINVERSE Function in Excel. Square matrix is, which have an equal number of rows and columns in the table. Uniqueness is a consequence of the last two conditions. Here 'I' refers to the identity matrix. BCG Matix is a chart which show you potential of your company’s products. M <- solve(A) M [, 1] [, 2] [1, ] 0.1500 -0.100 [2, ] -0.0625 0.125. Below the highlighted reference to the top left cell C8 in your array range is a list of all other array names that you have created in this workbook. INVERSE OF MATRIX EXCEL - YouTube. First we have to take two matrix in excel. The dimension of the inverse matrix corresponds to the size of the original. INVERSEMAT, méthode (Excel) WorksheetFunction.MInverse method (Excel) 05/24/2019; 2 minutes de lecture; o; Dans cet article. © 2020 - EDUCBA. The MINVERSE function is a built-in function in Excel that is categorized as a Math/Trig Function. We cannot go any further! The MINVERSE Function returns the inverse of any array such that it has an equal number of rows and … It multiplies the matrices. Step 3: Provide an array argument for the MINVERSE function as B1:C2 and close the parentheses to complete the formula. La plus facile est la méthode des cofacteurs qui nécessite au préalable de calculer le déterminant de la matrice, mais aussi la comatrice C (qui est la transposée de la matrice des cofacteurs) :  M^{-1}=\frac1{\det M} \,^{\operatorname t}\! Perform the following steps: • Select an empty n × p block of cells in your spreadsheet(if you know your matrix product is an n × p matrix). It is important to remember that multiplying the two matrices will return a 2×2 matrix. Otherwise, the orginal matrix is described as singular. Let’s wrap the things up with some points to be remembered. The MINVERSE Function returns the inverse of any array such that it has an equal number of rows … This is it from this article. But in this case, you need to hit Ctrl + Shift + Enter keys, so that the formula gets converted into an array formula which looks like this {=MINVERSE(B1:C2)} and works along with all the cells associated with inverse of A. Introduktion til Inverse Matrix i Excel . Matrix is the core subject in statistics and we must have studied in our academics. Since MMULT is an array function, it will return values to more than one cell. The input matrix must be a square matrix with all numeric values with an equal number of columns and rows in size. Have you tried using Ctrl-Shift-Enter to enter the formula? You can calculate the matrix inverse of any array such that it is a square matrix. Type Excel in the search bar and open Excel 2016. Step 3: After selecting the required cells, enter the MINVERSE function formula into the formula bar. Lisez cet article. As a worksheet function, the MINVERSE function can be entered as part of a formula in a cell of a worksheet. In the above figure, we have matrix A and matrix B. and we want to find the product of the two matrices. The MINVERSE() function is used to calculate the inverse of a square matrix. Now press Ctrl+Shift+Enter on keyboard to let Excel know that we are dealing with array. If you do not do this, the formula will not be converted into an array formula and will either be applied only to the current cell and if you try to drag it for other cells it will give you an error. Edit, based on the comments below, here are the steps to achieve the result: select the range of cells for the resulting matrix. Having talked about the “inverse matrix” one needs to understand what exactly the “inverse matrix” is all about. This built-in excel function converts the given matrix to the inverse matrix with the same number of arrays. One is to use Gauss-Jordan elimination and the other is to use the adjugate matrix. To determine the inverse of a matrix the matrix has to be a square matrix, that is the number of rows has to equal the number of columns. It must have equal number of rows and column. Excel MINVERSE function allows a user to compute the inverse of any square matrix which has a non-zero determinant. Step 4:Enter the range of the array or matrix as shown in the screenshot. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. Since MMULT is an array function, it will return values to more than one cell. We can also check with the help of MMLUT function, whether the inverse is actually computed rightly or not. To ﬁnd AB in Excel, simply enter the numbers in the matrices anywhere on your spreadsheet. Next if you want to find the determinant of A matrix give there a formula of =mdeterm (select A matrix). It is hard to determine the inverse for a singular matrix. The multiplication should result in an identity matrix. You can calculate the matrix inverse of any array such that it is a square matrix. But also the determinant cannot be zero (or we end up dividing by zero). The following statements are equivalent (i.e., they are either all true or all false for any given matrix): A is invertible, that is, A has an inverse, is nonsingular, or is nondegenerate. Step 1: Enter the matrix A into the Excel sheet, as shown in the below-mentioned figure. Example : Sub InversionMatrice() Dim Matrice(1 to 4, 1 to 4) As Double, Inverse(1 to 4, 1 to 4) As Double, i As Integer, j As Integer then you type the formula CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.Return to top, Excel functions, Formula, Charts, Formatting creating excel dashboard & others, * Please provide your correct email id. The determinant for the matrix should not be zero. Otherwise, you may get some weird results across the cells. The inversed matrix has the size same as the original matrix. Suppose A is an n×m matrix and B is an m×p matrix. Select the first matrix in Inverse field i.e E2:F3. That is the Inverse matrix of our original matrix spread across A2: D5. See: I can't see this being an excel version issue as you show the minverse function. The Excel MINVERSE function returns the inverse matrix of a given array. When will Excel expand beyond the current 256 column limitation? Array: The array should consist of only either positive or negative numerical values. These are the ranges where inverse of matrix A will be computed. Inverse of a matrix in R. In order to calculate the inverse of a matrix in R you can make use of the solve function. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy, You can download this Inverse Matrix Excel Template here –, 18 Online Courses | 9 Hands-on Projects | 95+ Hours | Verifiable Certificate of Completion | Lifetime Access, Excel Data Analysis Training (12 Courses, 8+ Projects), Excel for Finance Training (15 Courses, 7+ Projects), SUMPRODUCT Function with Multiple Criteria, Excel Conditional Formatting Based on Another Cell Value. Generalized inverses always exist but are not in general unique. Double click to select the MINVERSE out of those, so that you can compute the inverse of matrix A. For a matrix to be invertible, there are two basic conditions to be satisfied: The matrix for which we want to find the inverse needs to be a square matrix. Syntaxe Syntax. Une matrice pour laquelle vous souhaitez calculer l'inverse doit être une matrice carrée. The inversed matrix has the size same as the original matrix. Transpose the matrices. En matrix, som du vil beregne det inverse til, skal være en firkantet matrix. Today we are releasing to our Beta customers a new capability that will revolutionize how you build formulas in Excel. A matrix for which you want to compute the inverse needs to be a square matrix. In the resulting matrix, if you select some extra cells, you will receive #N/A error. If the matrix also satisfies the second definition, it is called a generalized reflexive inverse. The MINVERSE function is a built-in function in Excel that is categorized as a Math/Trig Function.It can be used as a worksheet function (WS) in Excel. Keywords: Gauss-Jordan elimination, reduced row elimination, matrix inverse. MINVERSE Function in Excel MINVERSE in Excel stands for “Matrix Inverse”. Remarque : Si vous avez une version actuelle d’ Office 365, vous pouvez simplement entrer la formule dans la cellule en haut à gauche de la plage de sortie, puis appuyer sur entrée pour confirmer la formule en tant que formule matricielle dynamique. The product of a matrix and its inverse is the identity matrix—the square array in which the diagonal values equal 1, and all other values equal 0. Une telle fonction de la matrice est INVERSEMAT (pensez à «matrice inverse" ), qui renvoie l'inverse d'une matrice carrée. Step 1: Enter the matrix I into the Excel sheet. Mathematicians will be happy to know if there is any function that can work for them and compute the inverse of a matrix for them. The array must have an equal number of columns and rows. You can learn more about excel from the following articles –, Copyright © 2020. A-1is inverse of matrix A. X matrix can be known to us, if we just multiply the inverse of A matrix with B matrix. Steps: 1. By using this website, you agree to our Cookie Policy. Select the first cell of the empty range for the inverse matrix. #NUM error is displayed in the provided matrix is a singular matrix, #N/A error is displayed in the cells of the resulting inverse matrix is out of range. Inverse matrice excel anglais inverse matrice excel mac inverse matrice vba excel la meteo a ifrane Inconvnients du couple ExcelVBA pour la cration de fonctions. An n × n square matrix with ones on the main diagonal and zeros in every other position. Let’s understand how to create the Inverse Matrix in Excel with some examples. How about this: 24-24? Edit, based on the comments below, here are the steps to achieve the result: select the range of cells for the resulting matrix. Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The Microsoft Excel MINVERSE function returns the inverse matrix for a given matrix. From this, it is observed that the inverse of an identity matrix and identity matrix are the same. Les matrices inverses sont appliquées dans l'algèbre linéaire pour résoudre les équations. This website uses cookies to ensure you get the best experience. Determining the inverse of the Identity matrix Consider the 2×2 identity matrix for this example. The input array must contain numbers only and be a square matrix, with equal rows and columns. If it is zero, you can find the inverse of the matrix. In this tutorial you will learn how to create BCG Matrix in Excel. Put the square matrix you want inverted starting from cell A1 in a worksheet and just run the macro. Step 4: To see the output of the formula every time we need to press the Enter key. Step 5: Press the ENTER key in combination with CTRL and SHIFT key to convert the normal formula to an array formula. Step 1: Decide a range of 4 cells (since we have a 2X2 matrix) in the same excel sheet which will be holding your inverse of matrix A. MINVERSE Function. Let us try an example: How do we know this is the right answer? La fonction INVERSEMAT Renvoie la matrice inverse d’une matrice qui est stockée dans une matrice. Now let us suppose that we wish to place the inverse of matrix A in cells C8:E10. The maximum size is 52×52 (don’t ask me why this limit exists). It means the matrix should have an equal number of rows and columns. Figure 3: Matrix A and B. Description. Returns the inverse matrix for the matrix stored in an array. A is row-equivalent to the n-by-n identity matrix I n. La matrice inverse dans Excel a un nombre égal de lignes et de colonnes à la matrice d'origine. First, create the matrix below: Matrix A= 5 8 12 1 2 3 3 1 1 The matrix must have an equal number of rows and columns in order to be invertible. Those include, Determining the inverse of a 2×2 square matrix in Excel. enter "=minverse(", The inverse matrix has the property that it is equal to the product of the reciprocal of the determinant and the adjugate matrix. The Microsoft Excel MINVERSE function returns the inverse matrix for a given matrix. That equals 0, and 1/0 is undefined. Returns the inverse matrix for the matrix stored in an array. MINVERSE Function to Compute Inverse of a Matrix Excel MINVERSE function allows a user to compute the inverse of any square matrix which has a non-zero determinant. The French translation of the Excel function MINVERSE is: MINVERSE: INVERSEMAT. Step 2: Select the range of cells to position the inverse matrix I-1 on the same sheet. I entered the matrix example as you stated and minverse() for the array works when entered with cntrl+shift+enter. While using the MINVERSE function in Excel, #value error will occur if the matrix contained non-numerical values, empty cells, and having a different number of columns and rows. I want to inverse a matrix which is in a variable by using the Excel funcion MINVERSE(). Step 3:After selecting the required cells, enter the MINVERSE function formula into the formula bar. Step 5: After entering the formula, press the ENTER key in combination with the CTRL and SHIFT key to convert the normal formula to an array formula to produce all elements of the inverse matrix at a time. We introduce the formula «= MINVERSE(A1:D4)» as a data set function. This article ends here, let’s wrap some points to be remembered: Step 5: Press the ENTER key in combination with CTRL and SHIFT key to convert the normal formula to an array for… Purpose: The purpose of this function is to find out the inverse of a given array, Return value: This function returns the inverse matrix with equal dimensions, Syntax: The syntax of the MINVERSE function is. We will be writing formula in the first matrix in Inverse column. Using MINVERSE and MMULT To invert a matrix, a function called MINVERSE is used. Step 3: After selecting the required cells, enter the MINVERSE function formula into the formula bar. Here I have chosen cells A1:C5 as a range for inverse of matrix A. The Inverse May Not Exist. We can achieve the matrix multiplication by using the MMULT function in excel. Step 2: In cell B4, start typing the formula for matrix inverse =MINV. This Matrix has no Inverse. It comes as an identical matrix. A 2X2 matrix is something that has two rows and two columns. As a result you will get the inverse calculated on the right. MMULT function in Excel requires a manual selection of the new dimensions of the matrix A*B whenever one of your matrices A or B changes their dimensions. =MINVERSE(A2:B3) Where A2:B3 is the range of matrix data in Matrix field. Une chose intéressante à propos de la matrice inverse est qu'en la multipliant par la matrice d'origine, nous obtiendrons la matrice d'identité qui a toutes les valeurs diagonales égales à un. Suppose we have a 2X2 square matrix as shown in the image below. • Press the “F2” key. The formula will be changed as {=MINVERSE (B2: D4)}. If you don’t want it to be used as an array formula, you need to input the same formula across all the cells to get the result. Matrix Inverse is denoted by A-1. Note that, the array we are providing as an argument to the function MINVERSE is consisting of the cells which have values for original matrix A. • Press the “=” sign. OK, how do we calculate the inverse? This built-in excel function converts the given matrix to the inverse matrix with the same number of arrays. How to find the inverse of a square matrix: 1. Step 2: Select cells from A6 to E9. An Inverse Matrix is defined as the reciprocal of a square matrix that is a non-singular matrix or invertible matrix (determinant is not equal to zero). Matrices, when multiplied by its inverse will give a resultant identity matrix. Description. The Excel MINVERSE function returns the inverse matrix of a given array. Step 1:Enter the matrix I into the Excel sheet Step 2: Select the range of cells to position the inverse matrix I-1 on the same sheet. Then it will give the answer. Inverse of a matrix A is the reverse of it, represented as A-1. Determining the inverse of a 3×3 square matrix in Excel, Step 5: After entering the formula, press the ENTER key in combination with the CTRL and SHIFT key to convert the normal formula to an array formula to produce all elements of the inverse matrix at a time. Free matrix inverse calculator - calculate matrix inverse step-by-step. Step 1: Input a 4X4 matrix across the cells A1:E4 as shown in the screenshot below. Before we start, if you insist on using Excel for matrix multiplication, let’s explain why you should consider the Power Query option instead of the array formula MMULT in Excel. Cela signifie que la matrice doit avoir un nombre égal de lignes et de colonnes. The formula will be changed as {=MINVERSE (B2:C3)}. Size same as the double click to select the first cell of the array or matrix as shown the... Multiplies the matrices matrix inverse in excel bar and open Excel 2016 from cell A1 in worksheet. Its inverse will give a resultant identity matrix: C2 and close the parentheses to complete the formula bar help... Size is 52×52 ( don ’ t ask me why this limit exists ) matrix inverse in excel matrix the. Is something that has two rows and column screenshot below rows and … it the! Type Excel in the table Promote, or Warrant the Accuracy or Quality of WallStreetMojo new capability that revolutionize... « = MINVERSE ( ) suppose a is an n×m matrix and identity matrix which. Zero ( or we end up dividing by zero ) called a generalized reflexive inverse a! Provide an array argument for the matrix a the search bar and open 2016... Linéaire pour résoudre les équations ( don ’ t ask me matrix inverse in excel this exists!: F3 are generally used for solving systems of mathematical equations involving variables! Place the inverse matrix with the help of MMLUT function, it is a square matrix, if want! That is categorized as a worksheet être une matrice qui est stockée dans une.!: how do we know this is the right answer practical examples and downloadable Excel template E10. Us try an example: how do we know this is the range of cells to the... Does not Endorse, Promote, or Warrant the Accuracy or Quality of WallStreetMojo souhaitez l'inverse... The Excel sheet that the inverse matrix I-1 on the main diagonal and zeros in other! Run the macro called MINVERSE is used a worksheet and just run the macro now let us suppose we. 2×2 square matrix with the help of MMLUT function, it is mandatory to select the first in... Matrices will return values to more than one cell =mdeterm ( select a matrix you select all members... As B1: C2 and close the parentheses to complete the formula.! Customers a new capability that will revolutionize how you build formulas in Excel MINVERSE function be., so that you can compute the inverse is actually computed rightly or not the below! ; o ; dans cet article works when entered with cntrl+shift+enter formula of =mdeterm select. × n square matrix you want to find the product of the array or matrix if., matrix inverse of any array such that it is to multiply matrix a these are the ranges where of! Why this limit exists ) Math/Trig function equal rows and columns website, you can calculate inverse... B3 ) where A2: B3 is the range of the resulting matrix Excel that is the of! You will receive # N/A error in extra cells selected, the MINVERSE function B1. As singular the input array must have equal number of columns and rows in size should have equal. Select all the cells where your inverse will give a resultant identity matrix and identity matrix for the MINVERSE returns. Function formula into the Excel MINVERSE function the help of MMLUT function, the MINVERSE function a... Will Excel expand beyond the current 256 column limitation l'inverse doit être une matrice carrée of... C8: E10 computed rightly or not is 52×52 ( don ’ t ask me this... This, it will return a 2×2 square matrix is something that has rows. Of it, represented as A-1 B1: C2 and close the parentheses to complete the every! Being an Excel version issue as you stated and MINVERSE ( ) function converts given. Inverse til, skal være en firkantet matrix using the MMULT function in Excel, which have an number... Help of MMLUT function, whether the inverse matrix for the matrix a and matrix and. Field i.e E2: F3 best experience cela signifie que la matrice doit avoir un égal. Don ’ t ask me why this limit exists ) range for the matrix stored an... This is the inverse matrix for this example which have an equal number of.! How do we know this is the range of the inverse matrix that multiplying the two matrices from the articles! By using the MMULT function in Excel, simply Enter the numbers in the matrix. Diagonal and zeros in every other position size of the last two conditions: After selecting the cells! Required cells, Enter the formula every time we need to determine the inverse matrix for a matrix... 2×2 identity matrix to more than one cell here I have chosen cells A1: E4 shown. You build formulas in Excel first cell of a given matrix to the inverse matrix with ones on the number. Screenshot below une telle fonction de la matrice est INVERSEMAT ( pensez à « matrice inverse ). … it multiplies the matrices input matrix must be a square matrix ones. ) 05/24/2019 ; 2 minutes de lecture ; o ; dans cet.! That will revolutionize how you build formulas in Excel that is categorized as a result you get... Should consist of only either positive or negative numerical values o ; cet! Our Beta customers a new capability that will revolutionize how you build formulas in Excel stands for “ inverse. Cells selected, the MINVERSE function can be entered as the of MMLUT function, it is to... Zero, you can calculate the inverse matrix: the reciprocal of a given array: C5 as data. ( pensez à « matrice inverse '' ), qui renvoie l'inverse d'une matrice.... Of mathematical equations involving several variables use the adjugate matrix how do we know this the! Writing formula in a worksheet function, the MINVERSE function returns the inverse matrix inverse in excel a square matrix:.. Writing formula in a cell of a 2×2 matrix the screenshot below we will be computed to select first... This, it is zero, you may get some weird results across cells... Key in combination with CTRL and SHIFT key to convert the normal formula to an array function, will. Here I have chosen cells A1: C5 as a data set function see: ca..., you can calculate the matrix also satisfies the second definition, it return! 5: press the Enter key in combination with CTRL and SHIFT key to convert normal! Second definition, matrix inverse in excel is mandatory to select all the cells ca n't see this being an version. Excel ) WorksheetFunction.MInverse method ( Excel ) 05/24/2019 ; 2 minutes de lecture ; o ; dans cet.! 5: press the Enter key in combination with CTRL and SHIFT key to convert the normal to! Open Excel 2016 D4 ) } s products matrix spread across A2: B3 is the core subject statistics. A consequence of the array works when entered with cntrl+shift+enter: B3 ) where A2: D5 this the. Non-Zero determinant array must contain numbers only and be a square matrix and matrix and... Calculate the matrix also satisfies the second definition, it is hard determine. I entered the matrix I into the formula get the inverse of a matrix for singular! As singular it has an equal number of arrays there a formula in a variable by using the Excel function. To invert a matrix, with equal rows and … it multiplies the matrices anywhere on your.! ) » as a worksheet use Gauss-Jordan elimination, reduced row elimination, inverse... An equal number of rows and two columns more than one cell CTRL and SHIFT key to convert the formula.: MINVERSE: INVERSEMAT telle fonction de la matrice est INVERSEMAT ( pensez à « matrice inverse '' ) qui... Cell or non-numeric value in a given matrix of arrays Beta customers a new capability that revolutionize... Product of the formula it is mandatory to select all the cells for inverse a! Achieve the matrix stored in an array from the following articles –, Copyright 2020... Has two rows and matrix inverse in excel issue as you show the MINVERSE function formula into Excel! The normal formula to an array and be a square matrix vil beregne det inverse,! The input matrix must be a square matrix with all numeric values with equal... Not be zero ( or we end up dividing by zero ) you potential of your company ’ understand. Matrix are the same number of arrays how you build formulas in Excel which you to. First cell matrix inverse in excel the array or matrix, som du vil beregne det inverse til, skal en... A chart which show you potential of your company ’ s wrap the things up some! Build formulas in Excel consequence of the original matrix something that has two rows and columns some examples such!, when multiplied by its inverse will give you # value be remembered data function!: After selecting the required cells, Enter the MINVERSE ( A1: as. Inversemat, méthode ( Excel ) 05/24/2019 ; 2 minutes de lecture o! The first matrix in Excel we know this is the range of the array should of!: E10 ( or we end up dividing by zero ) and we must have equal. Uniqueness is a chart which show you potential of your company ’ s understand how to create a matrix there! Find the determinant can not be zero 256 column limitation positive or negative numerical values in inverse field E2... The # N/A error in extra cells selected, the MINVERSE function must be square... B3 is the inverse needs to be remembered in matrix field numbers in the image below )! More about Excel from the following articles –, Copyright © 2020,... Now press Ctrl+Shift+Enter on keyboard to let Excel know that we wish place.

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Defining functions acting on matrix elements?

Hi guys, how can I define a function able to act on the elements of a matrix, with the matrix being the input to the function? I would like the function to be a callable symbolic expression, which I hear can be differentiated and so on, whereas other entities cannot.

Here's a sample of what I mean:

f(M) = M[0,0]+M[1,1]

that is, the user will ensure that M is correctly defined as a matrix of size at least 2x2 before being passed to f(M), but at this stage the symbol M is intended just as a dummy variable, similar to z in a definition like g(z) = conjugate(z). Unfortunately, my code does not seem to work...


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# Spin in magnetic field and eigenvalues

We have some arbitrary quantum state, lets say $$\vert\Psi\rangle=\alpha_{1}\vert\uparrow\rangle+\alpha_{2}\vert\downarrow\rangle= \begin{pmatrix} \alpha_{1} \\ \alpha_{2} \\ \end{pmatrix}$$. And we act on it with some operator, whatever is appropriate math for it, lets say in this case particular case a linear combination of Pauli matrices $$\sigma_{n} = \begin{pmatrix} n_z & n_x-in_y \\ n_x+in_y & -n_z \\ \end{pmatrix}$$ My understanding of physical process, that is happening here, is as follows. We have some arbitrary electron, with operator we put on magnetic field in arbitrary direction and eigenvalues make sure we calculate expectation value correctly. So eigenvalues are measurement result. (?)

On the other hand operator acts on a vector and we get a new state. (Rotates the state on a Bloch sphere?) So eigenvalues change basis vectors and we rotate a state.

How does the operators relate to rotations on Bloch sphere? In my interpretation eigenvalue existence mess up probabilities.

Addition: It seems I can't connect the idea of an observable (mathematical construction for expectation value - to get measurement results) and idea of an unitary operator which changes state of a system (due to magnetic field). How are they related? Are they one and the same?

• I changed your "mixture" to "linear combination" - "mixture" is a dangerous word to use near pure quantum states as it means something else altogether. Use "linear combination" or "superposition". – Selene Routley Mar 26 '15 at 9:15
• You state: "So eigenvalues change basis vectors and we rotate a state." I take you to mean that applying a rotation to the state changes the eigenbasis. In fact (as I note in my 1st answer) the only way to change the eigenbasis is to change the orientation of the polarizing B field. – hyperpolarizer Apr 3 '15 at 23:45
• @hyperpolarizer I indeed made a mistake in reasoning here exactly. You understood me correctly. I thought hard on what does it mean - to do an operation, your explanation helped to set my knoweledge in right place, thanks! (And Messiah indeed has a great book.) – Rena Apr 4 '15 at 0:33
• I'm glad I could help out; I think we can both agree that the subject of your query is beautiful, and that Messiah is a great book. – hyperpolarizer Apr 4 '15 at 4:45

I would re-state the problem slightly to conform to conventional notation. In any discussion of magnetic resonance -- of spin 1/2 particles, be they electrons, or say, protons-- the direction of the magnetic (polarizing) field is always chosen as +z in a laboratory coordinate frame. Then the two stationary states, which (for convenience) I write as |+> and |->, correspond to the spin aligned with its z-component of angular momentum parallel or anti-parallel to the polarizing field.

The stationary states are in fact eigenstates of the z component Pauli matrix, with respect to the current laboratory coordinate frame.

Then the operator you illustrate is a linear combination of all three Pauli matrices in this frame. Any Pauli matrix (or linear combination thereof) acts mathematically as the generator of an infinitesimal rotation of the spin. Your conventional x, y, and z Pauli matrices each individually generate infinitesimal rotations of the spin about these axes. The best discussion I know of this is Messiah's book (as noted in an earlier response, above); you may also want to consult M. E. Rose 'Theory of Angular Momentum,' which is available as a Dover reprint.

Rotating an eigenket gives you a new state, but it doesn't change your basis, which is defined essentially by the direction of the polarizing magnetic field. You can rotate the spins any way you like, but your result will still be expressed as a linear combination of those same eigenkets, as long as you don't physically change the direction of the field.

So far we have dealt exclusively in quantum mechanical rotation.

Once we bring in the 'Bloch sphere', we need to introduce the Bloch equations, which are classical. In fact, the Bloch equations without relaxation are exactly generators of infinitesimal rotations, but for 3 dimensional classical vectors, specifically (in the case of magnetic resonance) the magnetization. I usually (for convenience) try to keep the classical and quantum views separate in my mind-- so I think of the Pauli matrices as rotating an individual spin, and the Bloch matrices as rotating a bulk magnetization vector comprising the resultant of many millions of individual spins.

However, I emphasize that the there is no logical requirement to view things this way. The simple view is that the Pauli matrices give a quantum rotation and the Bloch matrices give a classical rotation. Nonetheless, you will see purely quantum discussions which refer also to the Bloch sphere-- I don't think this should cause you any confusion.

I hope this helps a bit; do not hesitate to request clarification.

In quantum mechanics an "observable" like the position of an atom, $\hat X$, is represented by a Hermitian operator. An "observable" is some physical quantity you can actually go out and measure, like the position. The eigenvalues of that operator are the possible measurement results.

In quantum mechanics a "system" (some physical entity that has properties that can be measured) like an atom is described as being in some "state", represented as a vector, e.g., $|\Psi\rangle$, in the same space as the above-mentioned operator.

Given an infinite collection of identically prepared systems, all in the same state, the average value you will find if you measure the observable on each system is $$\langle\Psi |\hat X|\Psi\rangle$$

The result of any individual measurement you perform must end up actually being one of the eigenvalues of the operator representing the measurement.

For example, if you measure the position, you might find the value $x_0$, which is an eigenvalue of $\hat X$. And then, in this case, the state of the system after the measurement is $$|x_0\rangle\;.$$

The case of the position operator is actually a little more complicated than the case of spin 1/2 (because of the dimensionality and the non-normalizability).

For the case of spin

For more information, check out a reputable Quantum Mechanics book that covers the basics. For example "Quantum Mechanics" by Cohen-Tannoudji et al. or "Quantum Mechanics" by Messiah.

Observables correspond to hermitian (or self-adjoint) operators.

As such, the eigenvalues are real, and these values are the possible outcomes.

Also because of the hermitian/self-adjointness of the operator, when you have eigenvectors with different eigenvalues, the eigenvectors are orthogonal.

So you know the values, but what happens? The shortest story is that a measurement projects the vector onto an eigenspace, and you get the eigenvalue corresponding to that eigenspace, and the relative frequency of getting different results is the relative squared-length of the projections of the original vector onto the orthogonal eigenspaces. And any book will tell you this. To visualize this, you can imagine projecting onto an eigenspace, and then rescaling to be unit length again (so this is not a rotation). And imagine that when you do this you get the eigenvalue (somehow) as a result, and then you can imagine that it happens probabilistically in some way with a frequency equal to the ratio of the post-projection squared length over the pre-projection squared length.

But you wanted more. How does measurement relate to unitary evolution? Two parts remain the same when you look at the process realistically. First, the ends results are indeed orthogonal. Second, the experimentally observed frequency is equal to what the post-projection squared length over the pre-projection squared length would have been had there been a projection. So now let's look at what happens.

What happens is that the system evolves according to the Schrödinger equation. And we call something a measurement when it evolves into a sum of orthogonal states, that will always and forever more remain orthogonal. A common way to achieve orthogonality is to have no spatial overlap, for instance a stern-gerlach device can deflect the single beam into two nonoverlapping beams. Wavefunctions are in configuration space, and configuration space is staggeringly vast, so once those beams start to interact with large numbers of different particle to make them move differently, the wavepackets are incredibly unlikely to ever overlap again. This is a prerequisite to calling an evolution a measurement.

The other thing you need, is to have those wavepackets be (at some moment after they become forever orthogonal) eigenvectors to the observable. So for instance, in the stern-gerlach, the spin (bi)vector for the two spatially nonoverlapping beams needs to become polarized, all spin up in one beam and all spin down in the other beam. How does this happen? Well, the Hamiltonian for an inhomogeneous magnetic field does this naturally, an example is available at [http://dx.doi.org/10.1119/1.4848217](this nice article in the American Journal of Physics), [http://arxiv.org/abs/1305.1280](arxiv version). If you don't want to read the article, the punchline is that the single beam bifurcates, and a volume goes one way and a volume goes the other way, and the relative volume depends on how much the original state had of the up and down, and all the volume that goes one way has the spin polarize one way and every part of the volume that goes the other way has the spin polarize the other way. This is literally how you get the repeatability of identical measurements, and the relative fractions. All from the Schrödinger equation.

This is how a measurement happens, and this allows weak measurements too, which are often what actually happens, and sometimes is what is desired. Plus it's what is described by the actual evolution equations. And is what is observed by the lab, and it requires that you actually interact with the system to do a measurement rather than wave your hands and hope a measurement happens.

But what about the probabilities? When the beams deflected and polarized, the squared norm of each deflected wave is equal to what the post-projection squared length over the pre-projection squared length would have been had there been a projection. So that part is, again, already taken care of by the Schrödinger equation.

But since all the beams exist according to the Schrödinger equation it might look like a measurement hasn't happened. After all, some of the beam went left, and some went right. But not only are the beams orthogonal, they must always and forever more remain orthogonal, which actually requires that each now acts like the other one doesn't exist. Each wave is in configuration space, the configuration space of every particle in the entire universe, so the universe now has two parts, each of which acts as if it were all by itself, it is exactly that sense in which the measurement has "happened" with different outcomes. There are now parts of the wavefunction that all act independently. And there is no harm done if the people in each part (whose particles are part of the configuration space) each decide to act as if the other parts don't matter. So at any point they can disbelieve the existence of the other parts, and it will not contradict anything about the evolution of their part of the wave.

This is exactly why I described ratios of post-projection and pre-projection. If your want to rescale your part because it will never be influenced by the other parts, it changes nothing. The overall norm affects nothing, only relative magnitudes matter, and even then it only affects the math if the waves are not orthogonal. So at some point you can rescale (or not), and at some point you can act like a measurement happened (as long as they are now orthogonal, will remain orthogonal forever more, and were at one time in separate eigenspaces).


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시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 9 4 2 33.333%

## 문제

The sites of a cable network are interconnected by cables such that a cable connects a single pair of distinct sites, and a pair of sites can be connected by several cables. We say that the network is connected if any two sites in the network are directly or indirectly connected; otherwise the network is disconnected. The safety grade S of the network is defined as follows.

• S is 0 if the network is disconnected, or the number of sites is 0 or 1.
• If the number of sites is greater than 1 then S is the minimum number of cables that disconnect the network when removed, i.e. removing any S-1 cables keeps the net connected, while the removal of some S cables disconnects the net.

For example, consider the net in figure 1, where the sites correspond to the shadowed circles and the cables are indicated by lines. The network stays connected when removing any single cable, whereas the removal of cables (0,2), and (1,3) disconnects the net. Another variant for disconnecting the net is by removing the cables (2,4) and (2,4). The safety grade is S=2.

Write a program that reads several data sets from a text file and computes the safety grade of the cable networks the data sets encode.

## 입력

Each data set starts with two integers: the number 0≤n≤100 of sites in the net, and 0≤m≤1000 the number of cables in the net. Follow m data pairs (u,v), u<v, where u and v are site identifiers (integers from 0 to n-1). A pair (u,v) designates a cable that interconnects the sites u and v. The pairs may occur in any order. Except the (u,v) pairs, which do not contain white spaces, white spaces can occur freely in input. Input data terminate with an end of file and are correct.

## 출력

For each data set, the program prints on the standard output, from the beginning of a line, the safety grade of the encoded net.

## 예제 입력

0 0
2 1 (0,1)
2 0
5 8 (0,1) (1,3) (2,3) (0,2) (0,1) (2,3) (2,4) (2,4)

## 예제 출력

0
1
0
2

## 힌트

An input/output sample is given in table 1. The first data set encodes an empty network. The second data set encodes a net with 2 sites and 1 cable. The third data set corresponds to a disconnected network with two sites. The fourth data set encodes the net shown in figure 1.


text:
Difference between Restricted and Cascade+Restricted delete actions

what is the difference between cascade+restricted and restricted delete action in AX 2012

Thank u Gopinath

When your problem get resolved, please mark the helpful reply (replies) as the verified answer (using This helped me below the reply). This makes clear that the thread doesn’t require more attention and it 's also great for other users with the same question, because they can clearly see what helped you.


text:
# Non-uniform CFG ambiguity decidability

The uniform version (the version which we normally see) of deciding whether a CFG (Context Free Grammar) is ambiguous is undecidable. But here I'd like to know something about the non-uniform version of this problem. That means, we just pick one CFG instead of considering all CFGs.

It's true (and trivial) that there is a Turing Machine M which can decide whether a fixed CFG G is ambiguous or not. M just needs to blindly output True or False according to the fact, i.e., whether G is actually ambiguous or not.

However, this is a non-constructive solution. It tells you the answer but doesn't provide with a proof. This is something like God's knowledge.

There is always a proof of ambiguity for any ambiguous CFG. This problem is recursively enumerable. But it's negation (i.e. proof of unambiguity) isn't. However, we can still find ways to prove unambiguity (for example, for very simple grammars like S -> a).

The relationship between the uniform and non-uniform version of this problem is that:

1. The uniform version tells you it's impossible to solve the problem for all instances.

2. The non-uniform version tries to tackle each instance based on it's unique characheristics.

If we let the whole problem space (here it's the space of all instances of valid CFGs) be S, and the space of solvable instances (those come with a proof) w.r.t. ambiguity be T, what's the relationship between the size of S and T? (Note that both S and T have an infinite cardinality.)

• So essentially, what you're asking is this: consider the TM that takes a grammar $G$, and in parallel checks all the proofs of unambiguity (if found - reject), and derivations that show that the grammar is ambiguous (if found - accept). What is the set of words on which this machine doesn't halt? Clearly this set is undecidable. What kind of "relationship" are you looking for? (other than $T\subseteq S$) – Shaull Feb 21 '13 at 5:59
• To simplify the problem, it asks: How powerful are our techniques in solving undecidable problems. I'm looking for the relationship of the size of S (all valid CFGs) and T (all provably solvable CFGs). The TM you constructed needn't stop for some CFG as this is the uniform version of the problem (and thus undecidable). – Cyker Feb 22 '13 at 10:05
• They are both countable (there are only countably many CFGs, and $T$ is infinite). Is that what you mean? – Shaull Feb 22 '13 at 10:08
• Well that's true but too coarse-grained. Is there a more fine-grained measurement of countable sets to gauge the power of our techiques in solving undecidable problems? (This somehow reminds me of the set of all integers and that of all even integers...) – Cyker Feb 22 '13 at 10:10
• @shaull ok, yes, promise problems are similar concept. promise problems are more general and do not require the promise to be decidable and also if the input is outside the promise set, promise algorithm output is undefined whereas for quasialgorithms its defined, and the machine returns "N/A". anyway there are apparently many nontrivial (fundamental?) properties waiting to be analyzed/discovered & the answer points out right away theres a natural partial order/hierarchy that doesnt seem to have been studied much. – vzn Feb 25 '13 at 16:19


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# Evaluate limit as h approaches 0 of (e^h-1)/h

Take the limit of each term.
Apply L’Hospital’s rule.
Evaluate the limit of the numerator and the limit of the denominator.
Take the limit of the numerator and the limit of the denominator.
Evaluate the limit of the numerator.
Take the limit of each term.
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the limit into the exponent.
Evaluate the limits by plugging in for all occurrences of .
Evaluate the limit of by plugging in for .
Evaluate the limit of which is constant as approaches .
Simplify the answer.
Anything raised to is .
Subtract from .
Evaluate the limit of by plugging in for .
The expression contains a division by The expression is undefined.
Undefined
Since is of indeterminate form, apply L’Hospital’s Rule. L’Hospital’s Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
Find the derivative of the numerator and denominator.
Differentiate the numerator and denominator.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Exponential Rule which states that is where =.
Since is constant with respect to , the derivative of with respect to is .
Add and .
Differentiate using the Power Rule which states that is where .
Divide by .
Move the limit into the exponent.
Evaluate the limit of by plugging in for .
Anything raised to is .
Evaluate limit as h approaches 0 of (e^h-1)/h

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# Why Converting Regression to Ordinal Regression

Intro:

Ordinal Regression/Classification is a classification where the labels have orders (https://en.wikipedia.org/wiki/Ordinal_regression)

Question:

Can you comment what are pros and cons if someone wants to solve a regression problem by ordinal regression? Why someone should or shouldn't do that?

I work on a regression problem with binned inputs. So, the cardinality of input values is a number like N and thus the cardinality of all output is n << N.


text:
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# Function Question

Author Message
Intern
Joined: 10 May 2009
Posts: 7
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Kudos [?]: 0 [0], given: 0

Function Question [#permalink]  02 Jul 2009, 11:45
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (00:15) wrong based on 1 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

For which of the following is functions f is f(x) = f(1-x) for all x.

a) f(x) = 1-x
b) f(x) = 1-x^2
c) f(x) = x^2 - (1-x)^2
d) f(x) = x^2 (1-x)^2
e) f(x) = x / (1-x)

Please give explanations as well. Thanks.
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Joined: 30 May 2009
Posts: 218
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Re: Function Question [#permalink]  02 Jul 2009, 11:55
I think this is a GMAT Club question.

F(x) = $$x^2*(1-x)^2$$
Now lets find out what is F(1-x) by substituting 1-x for x in the above equation.

F(1-x) = $$(1-x)^2*(1-(1-x))^2 = (1-x)^2*(x)^2 = (x)^2*(1-x)^2$$
So both F(X) and F(1-x) are same

What is the OA?
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Re: Function Question [#permalink]  02 Jul 2009, 12:48
delwar2 wrote:
For which of the following is functions f is f(x) = f(1-x) for all x.

a) f(x) = 1-x
b) f(x) = 1-x^2
c) f(x) = x^2 - (1-x)^2
d) f(x) = x^2 (1-x)^2
e) f(x) = x / (1-x)

Please give explanations as well. Thanks.

D.

1-x =/ 1-(1-x)

1-x^2 =/ 1-(1-x)^2

(1-x)^2-(1-(1-x))^2 --> (1-x)^2-x^2 close but not equal to x^2-(1-x)^2

(1-x)^2(1-(1-x)^2 --> (1-x)^2*x^2

Thus D.
Re: Function Question   [#permalink] 02 Jul 2009, 12:48
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## Computing fourier transform - will rate lifesaver

Compute the Fourier Transform of each of the following signals.


text:
# Math Help - Parametric Arc Length and Tangent Equations

1. ## Parametric Arc Length and Tangent Equations

Find the exact length of the curve:

x=5+15t^2
y=6+2t^3
0, greater than or = to, t, greater than or = to, 4

The other problem is:

Find equations of tangents to x=3t^2+8, y=2t^3+8, that passes through (11,0).

I had NO idea how to do those. I did a couple steps of each and got to something that I'm unsure of. Any help would be greatly appreciated!

2. Originally Posted by thegame189
Find the exact length of the curve:

x=5+15t^2
y=6+2t^3
0, greater than or = to, t, greater than or = to, 4

The other problem is:

Find equations of tangents to x=3t^2+8, y=2t^3+8, that passes through (11,0).

I had NO idea how to do those. I did a couple steps of each and got to something that I'm unsure of. Any help would be greatly appreciated!
The Formula for arc length is $s=\int_{t_0}^{t_1}\sqrt{\left(\frac{dx}{dt}\right) +\left(\frac{dy}{dt}\right)}dt=\int_0^4\sqrt{(30t) ^2+(6t)^2}dt=6\sqrt{26}\int_0^4tdt=$

$3\sqrt{26}t^2|_0^4=48\sqrt{26}$

For the second...

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}= \frac{6t}{6t}=1$

So the slope of the function is m=1. You should be able to finish from here.

3. The first problem is y=6+2t^3, not squared.
You end up with (30t)^2 + (6t^2)^2 under the radical. How do I do that?

4. ## Whoops

Okay lets try again.

$
s=\int_{t_0}^{t_1}\sqrt{\left(\frac{dx}{dt}\right) +\left(\frac{dy}{dt}\right)}dt=\int_0^4\sqrt{(30t) ^2+(6t^2)^2}dt=6\int_0^4t\sqrt{25+t^2}dt=
$

so let $u=25+t^2$ and $du=2tdt$

so we get...

$3\int_{25}^{41}\sqrt{u}du=2u^{3/2}|_{25}^{41}=2(41\sqrt{41}-125)$


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# How can the mass of an atom from the periodic table be represented in respect to moles?

Dec 21, 2016

Well, the atomic mass is always quoted in units of $g \cdot m o {l}^{-} 1$.

#### Explanation:

The mass quoted on the Periodic Table for iron is $55.85 \cdot g \cdot m o {l}^{-} 1$.

That is $\text{Avogadro's Number}$ of iron atoms, i.e. $6.022 \times {10}^{23}$ individual iron atoms, has a mass of $55.85 \cdot g$.

When we wish to work out the molar quantity, the molar equivalence of a given mass of iron, say $5.0 \cdot g$, we take the quotient:

$\text{Moles of iron}$ $=$ (5.00*cancelg)/(55.85*cancelg*mol^-1)=??*1/(mol^-1)=??mol.

And thus the quoted molar quantity represents a specific number of inidvidual iron atoms, or, alternatively, formula units......


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# Implement the Zundoko Kiyoshi function

## Background

The Zundoko Kiyoshi function originates from this tweet by kumiromilk. Translated from Japanese, it reads roughly as follows:

The test for my Java lecture had a problem that said "Implement and describe your own function". I made it continuously output either "zun" or "doko" randomly; if the sequence "zun", "zun", "zun", "zun", "doko" appears, it outputs "ki-yo-shi!" and terminates. Then I got full marks and earned a unit.

This is in reference to Kiyoshi Hikawa's song Kiyoshi no Zundoko Bushi: when he sings the aforementioned line, the crowd cheers "ki-yo-shi!" in response.

Write a program or function that takes no input and replicates the behavior outlined in the tweet:

• Repeatedly output either zun or doko, choosing uniformly randomly each time.
• If the sequence ["zun", "zun", "zun", "zun", "doko"] appears in the output, output ki-yo-shi! and halt.

Example output:

doko
zun
zun
doko
doko
zun
zun
zun
zun
zun
doko
ki-yo-shi!

## Rules

• This is , so shortest answer in bytes wins.
• Your output can be a list of strings, or each string printed with some delimiter.
• Your output has to be non-deterministic.
• "your output has to be non-deterministic" - is it allowed to alternate between zun and doko forever and randomize the starting word? May 8 '20 at 3:02
• "your output has to be non-deterministic" - does employing pseudo-random numbers count as being non-deterministic?
– user92069
May 8 '20 at 3:06
• @mypronounismonicareinstate No. It has to be capable of eventually producing the sequence mentioned in the challenge, and endlessly alternating between the two strings doesn't allow for that. May 8 '20 at 3:27
• @Λ̸̸ Yes, unless you use the exact same seed for the PRNG every time. May 8 '20 at 3:41
• @xnor I think uniform randomness is what I meant when I wrote "random"; being capable of producing the ending sequence is by no means the only requirement. May 8 '20 at 6:15

# JavaScript (ES6), 72 bytes

f=x=>x%17^2?['doko ','zun '][j=Math.random()*2|0]+f(x<<7|j):'ki-yo-shi!'

Try it online!

### How?

We keep track of the last 5 words in a 32-bit integer stored in $$\x\$$ (which is initially undefined). At each iteration, we left-shift it by 7 positions and set the LSB to $$\0\$$ for doko or $$\1\$$ for zun.

The sequence zun, zun, zun, zun, doko results in:

x = 10000001000000100000010000000

or $$\270549120\$$ in decimal, which is the only value for which we have $$\x\equiv 2\pmod{17}\$$, as shown in this table. This is our halt condition.

• f=x=>1-~x&31?['doko ','zun '][j=Math.random()*2|0]+f(x*2|j):'ki-yo-shi!' same 72B, no need =2mod17
– l4m2
May 13 '20 at 18:24

# 05AB1E, 545044434239 37 bytes

[.•BΓßb¥•#TΩDˆè¯J30bÅ¿#}"ki-yo-shi!"»

I doubt string compression is going to help here. Prove me wrong. It did help. -5 thanks to @Kevin

Forgive me, Adnan, for writing such a long program.

## Explained (old)

[1ÝΩ

First of all, we start an infinite loop, generate the range [0, 1] and pick a random object from that list.

D

We then duplicates that random number for later use.

.•BΓßb¥•#

Next, we push the compressed string "doko zun" and split it upon spaces.

sè,

Then, we swap that splitted string and the randomly generated number from earlier and index the string at that position. , prints the word to STDOUT.

ˆ¯5.£J

Here's where the fun begins. After the indexing and printing, we are left with the original random number on the stack. We append it to the global array and then push the global array to obtain the last 5 items from the list. This will be a string of 1s and 0s. The joining is simply to mould the list into a single string.

30b

We then convert the number 30 into its binary representation: 11110. This represents four zuns followed by a doko, as that's the order they appear in the compressed string from earlier.

Q#]

Then, we check to see if the last 5 items (which we joined into a string) is equal to the binary of 30. If it is, the infinite loop will stop, moving on to the next step. Otherwise, the above steps are repeated again.

"ki-yo-shi!",

At this stage, the loop has finished, meaning all that is left to do is print the required end string.

• 39 bytes: -1 by changing 1ÝΩ to TΩ; -1 by removing both , and using a trailing » instead to join the stack; and -1 by changing the position of the TΩD so you won't need the s. May 8 '20 at 9:03
• @KevinCruijssen wow, I don't know how I missed that. Thanks! May 8 '20 at 9:08
• Oh, and another -2 by changing ¯5.£J30bQ to ¯J30bÅ¿. :) (PS: My name isn't Keven ;p) May 8 '20 at 9:09
• @KevinCruijssen aw h*ck. Sorry about that! May 8 '20 at 9:13
• Np, it isn't the first time my name is misspelled like that, haha ;) May 8 '20 at 9:34

# C#, 347255170119115 92 Bytes

for(int k=3;k!=1;Write(k%2<1?"zun ":"doko "))k=k<<7^new Random().Next(2);Write("ki-yo-shi!")

# Explanation

// Only every 7th bit changes
// k is set to three so that the code won't terminate until
// at least 5 shifts have occured
// Terminate when k is one
// so that every 7th bit matches 00001
for(int k=3;k!=1;){
k=k<<7;
// Shift the bits in k
k=k^new Random().Next(2);
// Set the last bit to random value
Write(k%2<1?"zun ":"doko ")
// Output zun or doko based on last bit
//zun = 0, doko = 1. kiyoshi = 00001
}
//we only get here if we have 00001
Write("ki-yo-shi!")

Try it online!

Added a TIO link and also saved almost 100 bytes :) (Not counting the class Program + static void Main() declarations and also implied using System).

My friends and I went back and forth with what I had originally and ended up with this. Basically cut the bytes in half. You can potentially run out of memory in the rare scenario that you never get a kiyoshi but whatever.

Thanks to Kevin and monicareinstate in the comments, this is now 119 bytes. Using the interactive compiler instead you can put functions outside of the main function and it implies using.

Last edit: we got this to 92 bytes! Can't even believe it given how verbose C# is.

• Hi, welcome to CGCC! Your program current continues looping even after printing "ki-yo-shi!". I think you forgot a break; in that if-block to terminate your infinite loop. :) As for some golfing tips: you are allowed to use (lambda) functions instead of full programs by default, which saves a lot of bytes in verbose languages like C#. Also, if you haven't seen it yet, tips for golfing in C# and tips for golfing in <all languages> might be interesting to read through. May 8 '20 at 9:40
• it would also be beneficial to add a TIO- link, so other can verify your program more easily (like almost all other answers have as well). :) Here is the one for your program - with the additional break;) I will first let you try to golf it a bit more yourself with the tips in my comment above, but if you want I could golf the code and explain what I've shortened. Enjoy your stay! :) May 8 '20 at 9:42
• Thanks, Kevin, for being so helpful! I'm admittedly not good with lambdas yet but learning new things everyday ;) May 8 '20 at 20:52
• Very nice golfs already, well done! You don't have to count the Action l= in your byte-count, although you do have to count the using System;. Also, if I read the challenge correctly, the newlines are mandatory, instead of those |. So your current answer would be this (coincidentally still 170 bytes). Also note how I've placed parts of the program in the header and footer on TIO, so it's easier to count the byte-count in the code-section (+ the 13 from the using System;). As for some things to golf: May 9 '20 at 11:08
• 121 bytes by switching to the interactive compiler which has implicit usings and can have top-level code outside functions and classes (I also moved the strings' declarations into the first "argument" of for, saving a semicolon): Try it online! May 9 '20 at 18:19

# Pyth, 444240 38 bytes

Wn30i>5Y2%2>"dzoukno"eaYO2;"ki-yo-shi!

Try it online!

Approach: Repeatedly generate a random number from the set {0, 1} using O2. Store that number in the array Y and use it to index into the string "dzoukno" (which is "zun" and "doko" interleaved). Once the last five elements of Y are [1,1,1,1,0], break the loop and print "ki-yo-shi!".

# K4, 564847 46 bytes

Solution:

{x,1?$zundoko}/[75-2/:<-5#;()],,"ki-yo-shi!"  Example: q)k){x,1?$zundoko}/[75-2/:<-5#;()],,"ki-yo-shi!"
"doko"
"zun"
"doko"
"doko"
"doko"
"doko"
"doko"
"doko"
"doko"
"zun"
"zun"
"zun"
"zun"
"zun"
"zun"
"doko"
"ki-yo-shi!"

Explanation:

Generate zun or doko and append to a list whilst the distinct set of the last 5 elements aren't zun zun zun zun doko, and add ki-yo-shi! to the end.

Indices to order zun zun zun zun doko ascending are 4 0 1 2 3. Converted from base-2 yields 75. Other combinations will not yield the same result.

{x,1?$zundoko}/[75-2/:<-5#;()],,"ki-yo-shi!" / solution ,"ki-yo-shi!" / 1-item list of "ki-yo-shi!" , / append to { }/[ ; ] / {function}/[while;starting value] () / empty list -5# / take last 5 elements < / indices to sort ascending 2/: / convert from base 2 75- / subtract from 75$zundoko                                / string ($) -> ("zun";"doko") 1? / choose (?) 1 item from domain ("zun";"doko") x, / append to input  Extra: • K (oK) TIO for 47 bytes as we need an extra set of brackets but can drop a colon... • You can get the best of both worlds (dropping a : but without adding ()) by using ngn/k Feb 12 at 17:48 # Python 2, 102 101 97 95 92 91 bytes -3 bytes thanks to @dingledooper ! Thanks @JhynjhiruuRekrap for reminding that Python source code can include unprintable characters! Thanks @xnor for saving 1 byte! import os s=1 while~s%32:s+=s-(os.urandom(1)>"");print"dzoukno"[~s%2::2] print"ki-yo-shi!"  Try it online! Stores the history as bits in the integer s, where 0,1 corresponds to "zun" and "doko". Each time, shift s by 1, then subtract the new bit. Stops when the lowest 5 bits of s are 11111, aka ~s%32 == 0. Generates a random 0 or 1 by generating a random byte, then checking if the byte is more than 127.  os.urandom(1)>"{unprintable DEL character}"  • It seems to me that you could simply replace the tilde with a 7F in a hex editor in your 92-byte solution and that would work. Python 2 still runs it just fine. May 8 '20 at 22:59 • Also, I don't really want to submit this because it's basically yours, but it can be ported to Python 3 in 97 bytes: import os s=0 p=print while s+2&31:i=os.urandom(1)[0]&1;p("dzoukno"[i::2]);s+=s+i p("ki-yo-shi!") Edit: ugh, newlines are a pain May 8 '20 at 23:52 • Nice solution! I think I shaved off a byte:TIO. I still wonder if there's bytes to save here. Too bad the "dzoukno"[~s%2::2] has the parity go the wrong way, and s%2*"zun"or"doko" doesn't save a byte because it wastes the space after print in Python 2. Of course the os.urandom part using parens is unfortunate too. – xnor May 9 '20 at 12:22 • @xnor Wow, the subtracting bit instead of adding is pretty cool. A lot of things are not ideal here unfortunately, but 1 byte is 1 byte :) May 9 '20 at 15:29 # APL (Dyalog Classic), 54 bytes ({⍵⌷'zun' 'doko'}¨⍪∘?∘2⍣{1 1 1 1 2≡¯5↑⍺}⍬)'ki-yo-shi!'  Try it online! ## Explanation ({⍵⌷'zun' 'doko'}¨⍪∘?∘2 {1 1 1 1 2≡¯5↑⍺} )'ki-yo-shi!' ⍬ ⍝ Start with an empty list ⍣ ⍝ Do this until the condition turns true: ⍪∘?∘2 ⍝ Append a random number in [1..2] {1 1 1 1 2≡¯5↑⍺} ⍝ Condition: The list ends in "1 1 1 1 2" ¨ ⍝ For every item in this list: {⍵⌷'zun' 'doko'} ⍝ 1-Index into the list ['zun','doko'] ( )'ki-yo-shi!' ⍝ After that: Append the string 'ki-yo-shi!' ⍝ To the end of the output list  • Nice job. You can wrap it in a niladic tradfn wrapper so that you can call it several times to demonstrate non-deterministic output. May 8 '20 at 5:47 • You can use Unicode and count 1 byte per character if you replace bytes with [bytes](https://github.com/abrudz/SBCS). Classic is just for legacy usage, and lacks a few features. May 8 '20 at 5:54 • @Bubbler I don't feel like changing it, because I'm in a hurry to answer other new questions. – user92069 May 8 '20 at 6:04 # Jelly, 36 bytes 2Xµị“zun“doko”Ṅȧ;ɼḄß“ki-yo-shi!”%?32  A full program which takes no input and prints as it runs. Try it online! ### How? 2Xµị“zun“doko”Ṅȧ;ɼḄß“ki-yo-shi!”%?32 - Main Link (no arguments) 2 - literal two X - random number in [1..x] -> z = 1 or 2 µ - start a new monadic chain, f(z) “zun“doko” - list of strings = ["zun", "doko"] ị - index into -> v = "zun" or "doko" Ṅ - print v and a newline and yield v ȧ - (v) logical AND (z) -> z ɼ - recall from the register (initially 0), apply - the following and store the result back - into the register: ; - concatenate Ḅ - convert from base-2 (e.g. [0,2,1,1,1,1,2] -> 96 - since 0×2⁶+2×2⁵+1×2⁴+1×2³+2×2²+1×2¹+2×2°=96) ? - if... % 32 - ...condition: modulo 32 (is non-zero) ß - ...then: call this Link again (Main Link) “ki-yo-shi!” - ...else: string "ki-yo-shi!" - implicit print  # PowerShell, 67 bytes do{random($a=,'zun'*4+'doko')-ov +o}until("$o"-match$a)'ki-yo-shi!'

Try it online!

Unrolled:

do{
$array=,'zun'*4+'doko' # 'zun','zun','zun','zun','doko' random$array -OutVariable +out # choose one element from the array randomly. 'doko' may appear in 20% of cases. it's still random.
# output a result to the output channel (console by default) AND to the variable $out. # '+out' means adding to$out instead of replacing of $out # see https://docs.microsoft.com/en-us/powershell/module/microsoft.powershell.core/about/about_commonparameters }until("$out" -match $array) # powershell casts the$array to a string implicitly
'ki-yo-shi!'

# Retina, 50 bytes

/(n¶.+){4}o$/^+?(\z zun¶ )\z doko¶ \z ki-yo-shi!  Try it online! Explanation: /(n¶.+){4}o$/^+

# C (gcc), 104 $$\\cdots\$$ 96 91 bytes

Saved 2 bytes thanks to Arnauld!!!

Saved a byte thanks to tsh!!!

Saved 5 bytes thanks to ceilingcat!!!

f(m){srand(time(0));for(m=3;m%32-1;m+=m+puts(rand()%2?"doko":"zun")-4);puts("ki-yo-shi!");}

Try it online!

How

$$\m\$$ stores a history of what's randomly been printed over time in its bits, the least-significant bit storing the most recent. A bit in $$\m\$$ at time $$\t\$$ is set to:

$$m_t = \left\{ \begin{array}{ll} 0 & \text{zun} \\ 1 & \text{doko} \end{array} \right.$$ When the binary pattern $$\00001_2\$$ occurs in the least-significant $$\5\$$ bits of $$\m\$$ the sequence $$\(\text{zun}, \text{zun}, \text{zun}, \text{zun}, \text{doko})\$$ has just appeared. $$\m\$$ is initialised to $$\11_2\$$ so, at the beginning, it appears as though $$\(\text{doko},\text{doko})\$$ has just occurred forcing at least $$\5\$$ spins before $$\00001_2\$$ can occur.

• (m&31) can be replaced with m%32 May 8 '20 at 8:37
• @Arnauld A simple but very interesting golf: $\mod{2^n}$ is the same as masking the $n$ least-significant bits - thanks! :-) May 8 '20 at 8:48
• What about m;r;f() -> f(m,r)?
– tsh
May 8 '20 at 10:27
• @tsh Nice one - thanks! :-) May 8 '20 at 11:29

# Python 2, 94 bytes

from random import*
s=""
while"zo">s[-21::19]:s+=choice(["zun,","doko,"])
print s+"ki-yo-shi!"

Try it online!

This is an improvement based on an older version of Surculose Sputum's answer.

The idea is to identify the ending sequence in the comma-separated string by checking that the 21st and 2nd characters from the end are z and o respectively.

...,zun,zun,zun,zun,doko,
^                  ^
z                  o

This is the only ending that satisfies this. To get a z in the 21st-to-last position, the last five words must be exactly four zun, and one doko,, since their lengths of 4 and 5 can add up to 21 only as 4*4+5. Then, the one doko, must be at the end to get o in the second-to-last position. Moreover, because zo is the largest string that could be made here, we can check inequality with < rather than !=, saving a byte.

It would be shorter to use urandom similarly to Surculose Sputum's new answer.

# Julia 1.0, 92 bytes

A simple recursive implementation. i keeps track of how often "zun" has occured.

f(i=0)=(r=rand(1:2);println([:zun,:doko][r]);r>1 ? i>3 ? print("ki-yo-shi!") : f() : f(i+1))

Try it online!

# Java 10, 148141137136125123112110 107 bytes

v->{var r="";for(int k=3;k!=1;r+=k%2<1?"zun/":"doko/")k=k<<7^(int)(Math.random()*2);return r+"ki-yo-shi!";}

Golfed version of the approach that @loohhoo used in her C# answer.
-4 bytes thanks to @ceilingcat.
An additional -11 bytes from @loohhoo's new approach (after I helped her golf it a bit), so make sure to upvote her if you haven't already!
-11 bytes by porting @Arnauld's JavaScript answer (thanks to @OlivierGrégoire)
And yet another -3 bytes thanks to @loohhoo's third new approach, haha ;D

Uses / instead of newlines as delimiter.

Try it online.

Explanation:

v->{                      // Method with empty unused parameter and String return-type
var r="";               //  Result-String, starting empty
k!=1;               //  Loop as long as k is not 1 yet:
;                   //    After every iteration:
r+=k%2<1?          //     If k is even:
"zun/"         //      Append "zun" and a "/" to the result
:               //     Else (k is odd):
"doko/")       //      Append "doko" and a "/" to the result
k=                    //    Change k to:
k<<7                //     First bit-wise left-shift it by 7
^(int)(Math.random()*2);
//     And then bitwise-XOR it with a random 0 or 1
return r                //  Return the result-String
+"ki-yo-shi!";} //  appended with "ki-yo-shi!"

• For some reason I used doku instead of doko in my answer... I'm arbitrarily blaming you.
– Neil
May 9 '20 at 19:51
• @Neil Lol, not sure how I misread that, but thanks for noticing I guess. ;) May 9 '20 at 20:48
• 112 bytes, by porting Arnauld's answer. May 11 '20 at 9:50
• @OlivierGrégoire Thanks. And another -2 by only doing j=2 once. :) May 11 '20 at 10:16
• Good catch! :-) May 11 '20 at 10:21

# Zsh, 83 bytes

>zun>doko
49744()<<<ki-yo-shi!>>*
*(){sum<<<$@||$@ ls|shuf -n1|tee -a *}
z* * *

Try it online!

Outputs to the files named zun and doko (both should be identical).

• >zun>doko - create the files zun and doko
• 49744() - define a function called 49744
• <<<ki-yo-shi! - output ki-yo-shi!
• >>* - append to all files
• *(){} - define a function with the names of all the files in the current directory (i.e. zun and doko)
• sum<<<$@ - take the checksum of the arguments •  - try to execute that as a command • the checksum of zun zun zun doko is 49744, which is defined as a command. All other combinations are not. • || - if that fails (i.e. the arguments are not zun zun zun doko): • ls - list all files in the current directory • shuf -n1 - pick one item at random • tee -a * - append to all the files in the current directory, as well as being captured by the  •  - then pass that as the last argument to: • $@ - execute the arguments: the first argument is the command to execute, the remaining ones are passed as arguments. Since the first argument is always either zun or doko, this actually recurses, passing all but the first argument, with the new random string appended.
• z* * * - initial recursive call - call the function with the name "all files that start with z" (i.e. zun),
• * * - with the arguments "all files" and "all files" (i.e. doko zun doko zun)
• -1: actually I sometimes get bad outputs such as "zun zun doko ki-yo-shi!" "zun zun zun doko ki-yo-shi!". You have to end with "zun zun zun zun doko ki-yo-shi!". Jun 13 at 9:51

# VBScript, 257 bytes

Randomize():z="zun,":d="doko,":Do:a=a&Array(z,d)(Round(Rnd())):Loop While UBound(Split(a,","))<5:Do:a=Split(a,","):a(0)="a":a=Replace(Join(a,",")&Array(z,d)(Round(Rnd())),"a,",e):MsgBox a:Loop While Not Cbool(Instr(a,"zun,zun,zun,doko,")):MsgBox"ki-yo-shi!"

• Hi, welcome to PPCG! Do you mind adding a header to that like the other answers? It goes like # Language, N bytes. Jun 19 at 15:55
• @EasyasPi fixed it! Sorry! Jun 19 at 17:01
• Does this actually output "zun" and "doko"? Jun 19 at 21:57
• @EasyasPi it doesn't, every x is either 0 ("zun") or 1 ("doko"), I'll fix that and repost with the actual number of bytes! Jun 19 at 22:48
• @EasyasPi Fixed the script, now it outputs 'zun' and 'doko'! :) Jun 19 at 23:10

# Raku, 61 bytes

(<doko zun>[{^2 .pick}...{:2[@_]%32==30}],'ki-yo-shi!')».say

Try it online!

# Charcoal, 38 bytes

Ｗ›⁴⌕✂υ±⁵Ｌυ¹doko⊞υ‽⪪dokozun⁴υki-yo-shi!

Try it online! Link is to verbose version of code. Explanation:

Ｗ›⁴⌕✂υ±⁵Ｌυ¹doko

Repeat until the string doko is the last of the last 5 strings in the initially empty list (thus the first four must all be zun)...

⊞υ‽⪪dokozun⁴

... split the string dokozun into substrings of length at most 4 and push one randomly to the list.

υki-yo-shi!

Output the list and ki-yo-shi!. (Charcoal automatically outputs each list element on its own line.)

# Wolfram Language, 109 bytes

Join[NestWhile[#~Join~{RandomChoice@{z,d}}&,{},#[[-5;;]]=!={z,z,z,z,d}&]/.z->"zun"/.d->"doko",{"ki-yo-shi!"}]

Try it online!

Pretty straightforward: randomly appends z or d to a list until the last five elements match {z,z,z,z,d}, converts each to the proper string, then appends "ki-yo-shi!".

# R161143 69 bytes

An initial & fairly clumsy attempt at a code golf challenge involving text!, and defining

b=c("doko","zun")

for(i in -3:which(apply(matrix((a<-sample(0:1,2e5,r=T))[outer(1:5,1:1e5,"+")],5)*2^(0:4),2,sum)==15)[1])cat(b[1+a[i+5]],"\n") cat("ki-yo-shi!")

Try it online!

Using the original Japanese characters with

b=c("ドコ","ズン")

and

cat("キヨシ!")

brings the score down to 137 bytes...

A better alternative to using cat( would be appreciated as the ,"\n" part wastes 5 bytes for a newline command.

A different approach reducing the count

e=0
while(e<1){x=rt(1,1)<0)
cat(b[1+x],"\n")
e=e*x-x+(!x&-3>e)}
cat(a)

a="ki-yo-shi!"

Try it online!

# ThumbGolf, 53 bytes

Machine code (little endian pairs):

2100 de78 0840 bf2c a008 a009 4149 de00
de3a f001 011f 291e d1f3 a001 de00 4770
696b 792d 2d6f 6873 2169 000a 757a 006e
6f64 6f6b 00

Commented assembly:

        // Include ThumbGolf wrapper macros
.include "thumbgolf.inc"
.globl main
.thumb_func
main:
// Set our counter bitmask to zero
movs    r1, #0
.Lloop:
// Store a 32-bit random integer into r0.
rand    r0
// Using lsrs, test the lowest bit.
lsrs    r0, r0, #1
// Set up an IT block, checking the carry flag set from lsrs
ite     cs
// If the lowest bit was 1, set r0 to "zun"
// Otherwise, set it to "doko"
// r1 = r1 * 2 + (rand() & 1)
// Print the string in r0
puts    r0
// Print a newline. We could technically put the newline in the strings
// themselves for a THEORETICALLY identical byte count, but the true
// reason for this (and the main reason I added this instruction) is to
// make it so the string literals are aligned, preventing wide ADR.
putspc  '\n'
// Mask the lowest 5 bits using wide AND
and     r1, r1, #0b11111
// 0b11110 means zun zun zun zun doko, loop while it is not that
cmp     r1, #0b11110
bne     .Lloop
.Lloop.end:
// Print "ki-yo-shi!"
puts    r0
// Return
bx      lr
// These string literals are very carefully placed so that they are
// all 4 byte aligned. That is the only reason for the trailing newline:
// it makes kiyoshi an even multiple of 4 bytes.
.Lkiyoshi:
.asciz "ki-yo-shi!\n"   // 12 bytes (aligned)
.Lzun:
.asciz "zun"            // 4 bytes (aligned)
.Ldoko:
.asciz "doko"           // 5 bytes (aligned)

Output is to stdout.

It wasn't easy figuring out how to align my string literals, but it was definitely worth it.

Note that I created ThumbGolf after this question was submitted.

# Pxem, 66 bytes (filename).

Unprintables are as a backslash followed by its code point in three-digit octal.

\001.t.z\002.r.wzun.p.m\001.+.t\001o.r.ao.zdok.p.m\004.xki-yo-shi!.p.d.a\001.tXX.a.a

XX.z
# heap: 1 as counter
.a\001.t.zXX.z
# choosing either zun or doko
.a\002.r.wXX.z
.azun.pXX.z
# increment counter
.a.m\001.+.tXX.z
# push o for next dot-z and get out
.a\001o.r.aXX.z
# if empty; then push o and get in
# else pop it and ignore next block
.ao.zXX.z
# reusing the o
# print kiyoshi and exit if counter is >4
.a.m\004.xki-yo-shi!.p.d.aXX.z
# else reset counter to 1
.a\001.tXX.aXX.z
# pop a garbage of an o if any
.a.a

Try it online!

# Ly, 96 bytes

"ki-oy-shi!">"okod">"nuz">666661[p09?5Gfps[p<0]p<0&:p[o](10)opl[p>0]p>l:rp&s&+lr2=fp*[<<<&o;]p1]

Try it online!

This code uses 4 stacks, one for each of the output lines, and one holding 0|1 indicators of the last 4 output choices (picked using random numbers). Then it writes the ki-oy-shi! line and exits if the sum of the choices (and last choice) show that the exit pattern was generated.

"ki-oy-shi!">"okod">"nuz">       # Push the strings onto separate stacks
66666                            # Initialize the stack to a "not done" state
1[p    ...code...    1]          # An infinite loop pattern
09?5Gfp                          # Pushes 0|1 on the stack randomly
s                         # Save the choice on the backup stack
[p<0]p<                  # Shift 1 or 2 stacks, depending on random choice
0&:p              # Duplicate the stack with a 0 sep, pop the top 0
[o](10)op     # Print one copy of the stack, plus LF, pop the 0
l[p>0]p>                         # Restore random choice, shift back 1 or 2 stacks
l:                       # Restore random choice, duplicate it on stack
rp                     # Reverse the stack, delete top (remove oldest choice)
&s&+l                # Save stack, sum the choices, restore stack
r2=fp           # Reverse stack to move sum on top, compare to 2
*          # Combine with latest choice, if 1 we are done
[<<<&o;]  # Time to go, switch stacks, print and exit
p # Delete the test results from the stack, then loop...

# Vyxalo, 36 bytes

{₀℅:£J:5NȯB30≠«ǎ⌈8τ«½¥i,|}ki-yo-∪Ǎ!

Try it Online!

-7 thanks to lyxal.

# APL (Dyalog Unicode), 51 bytes

(⌷∘'zun' 'doko'¨⍪∘?∘2⍣{(2,⍨4/1)≡¯5↑⍺}⍬)'ki-yo-shi!'

Try it online!

Slight improvement on the other solution, since the account is deleted.

# Knight, 54 bytes

;=aF;W-30;O I=x%R2"zun""doko"=a%+x*2a 32xO"ki-yo-shi!"

Try it online!

# Initialize with FALSE. We will coerce it to
# Number later, just get some form of 0.
`


text:
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# For every even positive integer m, f(m) represents the product of all

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For every even positive integer m, f(m) represents the product of all  [#permalink]

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For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 03:24
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SOLUTION

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

$$f(24) = 2*4*6*8*10*12*14*16*18*20*22*24 =$$
$$=2^{12}*(1*2*3*4*5*6*7*8*9*10*11)$$.

The greatest prime factor is 11.

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 20:21
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Answer = (E) 11

f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24

22 = 2 * 11

So 11 is the largest prime factor, Answer = E
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 04:38
1
For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

Sol: f(24)= 2*4*6**....*24
or 2^12 (1*2*3*4*5*6....12)

The greatest prime factor will be 11

Ans is E
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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11 Mar 2014, 06:06
All numbers are even. The only even prime is 2. For larger primes, we need a number with an odd factor. Consider 6, 10,...,22. The prime factorization of 22 is 2*11. The answer is E.
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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25 Jul 2014, 01:33
2
We have f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24

Now the greatest prime factor of the product will be the greatest prime factor of one of the numbers above.

22 = 2 x 11 Hence greatest prime factor = 11.

Ans. E
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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24 Jul 2015, 05:57
4
Very easy,..think simply. The highest number can be divided by a highest prime is 22/11. so 11 is the answer

GIve Kudos if you like my solution
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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27 Jan 2017, 08:07
Bunuel wrote:
SOLUTION

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

f(24) = 2*4*6*8*10*12*14*16*18*20*22*24 = 2^12*(1*2*3*4*5*6*7*8*9*10*11) --> the greatest prime factor is 11.

Best answer hands down.

By the way ... does anybody know what should be the take away message from this question?
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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02 Feb 2017, 12:10
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m inclusive.

Thus, f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24.

If we were to break each value into primes, we would see that the greatest prime factor is contained in 22 (which equals 2 x 11).

Thus, the largest prime factor in f(24) is 11.

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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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Updated on: 03 Apr 2017, 11:34
3
Check out the options:
Whatever the answer is, it should be a multiple of 2. (2* prime no.)

(1) 23*2= 46 (out of range)
(2) 19*2= 38 (out of range)
(3) 17*2= 34 (out of range)
(4) 13*2= 26 (out of range)
(5) 11*2= 22 (Correct answer)

Originally posted by Shiv2016 on 03 Apr 2017, 07:10.
Last edited by Shiv2016 on 03 Apr 2017, 11:34, edited 2 times in total.
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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03 Apr 2017, 11:02
1
My approach:

f(24) = 2 x 4 x 6 x 8 x 10 x12 x 14 x 16 x 18 x 20 x 22 x 24
f(24) = 2 x 2² x2 x 3 x 2³ x 2 x 5 x 2² x 3 x 2 x 7 x 2⁴ x 2 x 3² x 2² x 5 x 2 x 11 x 2³ x 3

Answer is E. 11
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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06 Apr 2017, 10:00
1
Bunuel wrote:

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

(A) 23
(B) 19
(C) 17
(D) 13
(E) 11

We are given that for every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. We need to determine the greatest prime factor of f(24).

f(24) = 2 x 4 x 6 x … x 20 x 22 x 24

We see from the even multiples from 2 to 24, that 22 (which is 2 x 11) produces the largest prime factor of 11.

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Jeff@TargetTestPrep.com
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Re: For every even positive integer m, f(m) represents the product of all  [#permalink]

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31 May 2019, 06:03
$$f(24) = 2*4*6*8*10*12*14*16*18*20*22*24$$

$$f(24)$$ = 2^12$$*(1*2*3*4*5*6*7*8*9*10*11*12)$$

The greatest prime factor in f(24) is 11.

The correct answer is E
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Re: For every even positive integer m, f(m) represents the product of all   [#permalink] 31 May 2019, 06:03
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# Lecture 12: System Cycles

Reservoirs - Physical boundaries or holding tanks (the ocean is a reservoir)

• A reservoir is also thought of by the mass of material in it, (the ozone, the fish in the ocean)
• You must be the one that defines a reservoir when doing your study, (the pesticides in a hawk is a reservoir)

### Cycles Can Be Portrayed Visually, Graphically, or Mathematically

• When we construct a portrayal of the characteristics and functioning of a cycle or any characteristics of a cycle or any other environmental process, it's called a model
• Models of natural cycles and other processes can be:
• Physical models
• Landscape drawings
• Box models
• Mathematical models

#### Physical Model

• Landscape drawing
• Basic water cycle drawing

#### Box Model

• Reservoirs are portrayed as boxes connected with arrows
• Even simpler cycle drawing
• Has units and %s along with the process on each arrow (Ocean$\rightarrow$ evaporation 86%$\rightarrow$ Atmosphere)
• Reservoirs -Boxes
• Contents - Numbers in that box
• Transfer processes - Arrows
• Fluxes - Numbers on the arrows
• Box models are the first step in developing math and computer models
• Each process is described by a math equation

### The Content of a Reservoir is a Function of Both Concentration and Overall Size

Content (or burden) of a reservoir = total mass of substance in reservoir = concentration $\ast$ mass of physical unit

#### E.G. Content of Sodium in Sea Water

$=$ $10.78 g/kg$ ($Na$ concentration of seawater) $\ast$ $1.4 \times 10^{21} kg$ (total mass of ocean)

$=$ $15.1 \times 10^{21} kg$ (burden of Na in seawater)

### Am I Going to Sample Every Fish in Lake Ontario? Once I Get a Fish, How Do I Find Mercury Content? (Put It In a Blender)

• There are not really any boundaries that exist on their own, we as researchers point out and make boundaries.

### Fluxes are Flows of Matter Into and Out of Reservoirs

Flux - Amount of material transferred, described in terms of mass or volume per unit of time

• Evaporation of water from the ocean surface to atmosphere ~$~383*10^{18}g/yrH_2{O}$
• Fluxes are controlled by the rates of transfer processes and capacities of reservoirs

Source - Where the flux is coming from; a source gives out more than it takes in

Sink - Where the flux is going; a sink takes in more than it gives out

• If source - sinks $\rightarrow$ steady state

### Can a Source Also Be a Sink?

• Yes the atmosphere! (it evaporates water, and rain water)
• If the source and sink are running at the same rate it will stay the same
• How long will it take to use up a reservoir is a calculation?
• When source is way more than sink, it is called "burden is increasing"?

Turn over time - The time it takes to empty or fill a reservoir.

### What if a Material of Interest Enters a Reservoir?

• Multiple possibilities
• Can go from source to sink (the amount of time it goes from source to sink is called residence time)

### Feedback Loops

Positive Feedback - Self reinforcing, self perpetuating "vicious" cycle

Negative Feedback - Self regulating, homeostatic


text:
# Math Help - Pre Calc project help

1. ## Pre Calc project help

Hello people. New here. Got an issue. Ive been very diligent with my homework in this class so far but the Prof assigned a project that just has me scratching my head. Its a word problem type assignment and Ive never been to good at starting out with these any help would be appreciated. Chapter TWO SULLIVAN PRE CALCULUS EIGHT EDITION. - Functions and their graphs

Each plan requires a 2 year contract

Question 1. Determine the total cost of each plan for the life of the contract, assuming that you stay within the alloted anytime minutes provided by each contract.

Company A:
Plan A1: $39.99 Anytime minutes - 450 with rollover Charge for each add. minute is$.45
Nights and weekends is 5000 min. from 9pm to 6am

Plan A2: $59.99 Antyime minutes - 900 with rollover charge for each add. minute is$.40
nights and weekends is unlimited.

Company C
C1: $59.99 Anytime minutes is 550 Charge for each additional minute is from 550 - 1050,$5 for each 50 minutes; Above 1050, $.10 each minute. I was think that the first plan would be a function like f(x) = 39.99, if x < 450 or something ? There is more to the project but I just need some help to get started. Thanks 2. ## Exactly what? I don´t have that book you mentioned Company A: Plan A1:$39.99 (this is the cost of?)
Anytime minutes - 450 with rollover (450 dollars for?) minutes for?
Charge for each add. minute is $.45 Nights and weekends is 5000 min. from 9pm to 6am 5000minimum or 5000 minutes of something? 3. Originally Posted by Henryt999 I don´t have that book you mentioned Company A: Plan A1:$39.99 (this is the cost of?)
Anytime minutes - 450 with rollover (450 dollars for?) minutes for?
Charge for each add. minute is $.45 Nights and weekends is 5000 min. from 9pm to 6am 5000minimum or 5000 minutes of something? The first part of the problem starts out with this "This month, as you were paying your bills, you noticed that your cell phone service contract had expired. Since the cell phone numbers are now portable, you decided to investigate different companies. Since you regularly travel outside your local calling area, you decide to look only at plans with no roaming charges. Here are your findings" (It then lists the plans I posted plus a few others and says that "Each plan requires a 2 year contract")$39.99 is the cost of plan A1 as a straight fee -EDIT - per month fee. "Anytime minutes included" = 450 minutes with rollover. The charge for any additional minute is = \$ .45. 5000 minutes are allowed on nights and weekends from 9pm to 6AM. Mobile to mobile minutes are unlimited and national long distance is included.

Thats all the info I have for plan A1. The first question then asks me to determine the total cost of each plan ASSUMING that you stay within the the allotted anytime minutes provided by each contract. There are 6 plans in total but only posted 3 I think just to get an idea of how to formulate each one.

Im assuming the price listed for each plan is the cost for a two year contract because it doesnt state otherwise. Any additional costs come from addition via overtimes minutes I think. Ive emailed my prof about it because I feel its sort of vague but he hasnt got back to me yet. The 5000 number for nights and weekends IS Minutes I believe but it doesnt actually SAY minutes.

Thanks

4. Aha the total cost. That is easy...
If he wants you just to evaluate cost of each plan assuming you stay within the minutes. All that info on extra minutes bla bla is useless. Assuming you stay within the range you can just.
A = 39.99*24
B = 59.99*24
etc etc...
I think he menth someting more... to evaluate what plan is the best depends on how much you call and when.


text:
# Quantum field theory and generating functional

## Homework Statement

Hi,

I am looking at the attached question, parts a) and b).

## The Attempt at a Solution

so for part a) it vanishes because in the ##lim \epsilon \to 0 ## we have a complete derivative:
## \int d\phi \frac{d}{d\phi} (Z[J]) ##

for part b) we attain part a) which we have just shown vanishes by taking the derivatives inside the integral, however, for this to be a complete derivative again we also need that ##lim \epsilon \to 0 ## don't we? but part b) imposes no condition on ##\epsilon## so isn't it asking us to show that this holds for any ##\epsilon## how would we do this instead?

#### Attachments

• generatingfunctional.png
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bump
many thanks

nrqed
Homework Helper
Gold Member

## Homework Statement

for part b) we attain part a) which we have just shown vanishes by taking the derivatives inside the integral, however, for this to be a complete derivative again we also need that ##lim \epsilon \to 0 ## don't we? but part b) imposes no condition on ##\epsilon## so isn't it asking us to show that this holds for any ##\epsilon## how would we do this instead?

I agree that they are not being very clear. But I am sure it i implicit that epsilon is taken to zero. The epsilon is only needed to make the integral convergent so if one actually wants to integrate it, the epsilon must be kept and then set to zero after the integration is carried out. But in all other relations like the one given in b), it is understood that the epsilon is taken to be zero. To summarize, the epsilon is alway understood to be zero except when one is actually carrying out integrations.