MathDB
P03 [Combinatorics] - Turkish NMO 1st Round - 2002

Source:

August 7, 2014

Problem Statement

In the beginnig, each unit square of a m×nm\times n board is colored white. We are supposed to color all the squares such that one of two adjacent squares having a common side is black and the other is white. At each move, we choose a 2×22 \times 2 square, and we color each of 44 squares inversely such that if the square is black then it is colored white or vice versa. For which of the following ordered pair (m,n)(m, n), can the board be colored in this way?
<spanclass=latexbold>a)</span> (3,3)<spanclass=latexbold>b)</span> (2,6)<spanclass=latexbold>c)</span> (4,8)<spanclass=latexbold>d)</span> (5,5)<spanclass=latexbold>e)</span> None of above <span class='latex-bold'>a)</span>\ (3,3) \qquad<span class='latex-bold'>b)</span>\ (2,6) \qquad<span class='latex-bold'>c)</span>\ (4,8) \qquad<span class='latex-bold'>d)</span>\ (5,5) \qquad<span class='latex-bold'>e)</span>\ \text{None of above}