This is a problem from my professor, who claimed that it's open:



> 
> Combinatorial problem.
> 
> 
> Fill $1,2,...,mn$ into a rectangle of size $m\times n$, such that for every number other than $mn$, there is a larger number which is in the same row or column.
> 
> 
> Prove there are $\frac{(mn)!m!n!}{(m+n-1)!}$ ways to fill.
> 
> 
> It is said that the problem is from a high school student.
> 
> 
> 


I would like to know:



> 
> Is the problem really open?
> 
> 
> If it's open, are there any references? Is it from a high school
> student, as claimed?
> 
> 
> 


There's no need to answer the problem to any extent.



Filling $1..mn$ into a $m×n$ rectangle such that every number $<mn$ is dominated
Here it is.


[Number of collinear ways to fill a grid](https://mathoverflow.net/questions/297385/number-of-collinear-ways-to-fill-a-grid?noredirect=1&lq=1)


