MathDB
tiling by dominoes and coprime numbers

Source: RS2004

March 20, 2005
number theorycombinatorics proposedcombinatorics

Problem Statement

An 8×88\times8 chessboard is completely tiled by 2×12\times1 dominoes. Prove that we can place positive integers in all cells of the table in such a way that the sums of numbers in every domino are equal and the numbers placed in two adjacent cells are coprime if and only if they belong to the same domino. (Two cells are called adjacent if they have a common side.) Well this can belong to number theory as well...