# Malcolm Gladwell's Outliers - Progressive Matrices Puzzle

In Outliers, Malcolm Gladwell presents the following puzzle:

 ♦♣♣ | ♥♥♣ | ♦♥♥
♦♦♣ | ♣♥♦ | ♦♣♣
♥♥♥ | ♦♦♣ | ♣♥♦
-----------------
♥♣♦ | ♥♣♦ | ♥♣♦
♥♣♥ | ♥♦♣ | ♣♥♥
♦♦♣ | ♣♥♦ | ♦♣♦
-----------------
♦♥♦ | ♦♣♥ |
♣♥♣ | ♦♥♦ |  ?
♥♣♦ | ♥♣♣ |


In the first edition (2008) of the book, the top left square erroneously appears as:

♣♣♦
♦♥♣
♦♥♥


The alleged answer in both cases is:

♥♦♣
♦♣♦
♥♥♣

I have two questions:

1. What is the pattern?
2. What mistake(s) could explain the discrepancy between editions?

Note: I have an answer for Q1, but do not have one for Q2.

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
001 | 120 | 011
222 | 001 | 120
-----------------
210 | 210 | 210
212 | 201 | 122
001 | 120 | 010
-----------------
020 | 012 |
121 | 020 |  ?
210 | 211 |


I found this quite simple algorithm (which has two cases, either it is a row change [type2] or not [type1]):

 Type 1:
* we (+1 mod 3) every element
* rotate columns left one step
* rotate last column upwards
Type 2, row change:
* rotate the matrix 90 degrees


Since the final step is type 1, we get

 120      120      120
200  ->  200  ->  202
112      112      110


and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
202  --> 010  -->  ♦♣♦
110      221       ♥♥♣


I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

1. What mistake(s) could explain the discrepancy between editions?

Printer error. The versions in the first and second editions swap multiple-choice answer H and the spurious NW-corner pattern.

Methodology:

Found versions that showed multiple-choice answers for the Outliers puzzle.

Incorrect First Edition version, as it appears at the link provided by Daedric:

Correct Second Edition version, presumably, as seen in a blog entry about Raven's Progressive Matrices:

The versions agree on every other pattern, including the correct multiple-choice answer A.

• I can confirm that is how it appears in the second edition. Great spot - I really should have noticed that! – Will Jan 28 '16 at 10:03
• Thank you for verifying this, @Will. It was clued in by the comment with the more-complicated solution referred to by CarlLöndahl, at the link provided by Daedric. I thought that this additional detective puzzle was an interesting change of pace and that you had omitted the multiple-choice answers just for that purpose. You can certainly bet that I (and others, no doubt) have had fun trying to make the odd pattern fit some algorithm as well. – humn Jan 28 '16 at 10:20

So I solved it a little differently:

If you look at the bottom left symbol on each of the patterns you’ll notice that each sign lines up with the pattern on the answer

• This is an interesting pattern, but to comprise an answer wouldn't the bottom row need to be three hearts? – Will May 26 '18 at 20:53
• Make sure to add spoiler tags >! at the beginning of the line – Redwolf Programs May 26 '18 at 21:19
1. List item

Without changing to numbers, you can use H,D,C for matrix in the same row with 1) last column shifts one left 2) new last columns shifts up one 3) clubs become hearts, hearts become diamonds, and diamonds become clubs.

For last transformation:

 DCH  CHD  CHD  HDC
DHD  HDD  HDH  DCD
HCC  CCH  CCD  HHC