MathDB
10th ibmo - chile 1995/q4.

Source: Spanish Communities

May 7, 2006
ceiling functionsymmetrycombinatorics unsolvedcombinatorics

Problem Statement

In a m×nm\times{n} grid are there are token. Every token dominates every square on its same row (\leftrightarrow), its same column (\updownarrow), and diagonal (\searrow\hspace{-4.45mm}\nwarrow)(Note that the token does not \emph{dominate} the diagonal (\nearrow\hspace{-4.45mm}\swarrow), determine the lowest number of tokens that must be on the board to dominate all the squares on the board.