Sudoku like grid: selection of n^2 cells
Source: ISI(BS) 2007 #8
April 12, 2012
combinatorics unsolvedcombinatorics
Problem Statement
The following figure shows a grid divided into subgrids of size . This grid has cells, in each subgrid.
[asy]
draw((0,0)--(9,0)--(9,9)--(0,9)--cycle, linewidth(2));
draw((0,1)--(9,1));
draw((0,2)--(9,2));
draw((0,3)--(9,3), linewidth(2));
draw((0,4)--(9,4));
draw((0,5)--(9,5));
draw((0,6)--(9,6), linewidth(2));
draw((0,7)--(9,7));
draw((0,8)--(9,8));
draw((1,0)--(1,9));
draw((2,0)--(2,9));
draw((3,0)--(3,9), linewidth(2));
draw((4,0)--(4,9));
draw((5,0)--(5,9));
draw((6,0)--(6,9), linewidth(2));
draw((7,0)--(7,9));
draw((8,0)--(8,9));
[/asy]
Now consider an grid divided into subgrids of size . Find the number of ways in which you can select cells from this grid such that there is exactly one cell coming from each subgrid, one from each row and one from each column.