Sum of black squares is equal to sum of white squares.
Source:
February 12, 2011
geometryrectanglenumber theory proposednumber theory
Problem Statement
In a multiplication table, the entry in the -th row and the -th column is the product From an subtable with both and odd, the interior rectangle is removed, leaving behind a frame of width . The squares of the frame are painted alternately black and white. Prove that the sum of the numbers in the black squares is equal to the sum of the numbers in the white squares.