We know the number of girls in every column and row
Source: IMO Longlist 1989, Problem 18
September 18, 2008
quadraticscombinatorics unsolvedcombinatorics
Problem Statement
There are some boys and girls sitting in an quadratic array. We know the number of girls in every column and row and every line parallel to the diagonals of the array. For which is this information sufficient to determine the exact positions of the girls in the array? For which seats can we say for sure that a girl sits there or not?