MathDB
P35 [Combinatorics] - Turkish NMO 1st Round - 2003

Source:

May 31, 2014

Problem Statement

n+m1n+m-1 unit squares are arranged in LL-shape whose one side contains nn squares and the other side contains mm squares. Ayse and Betul plays a turn based game with following rules: Ayse plays first. At each move, the player captures desired number of adjacent squares in same side of LL. The one who captures the last square loses the game. If four games are played for pairs (n,m)=(2003,2003)(n,m)=(2003,2003), (2002,2003)(2002,2003), (2003,3)(2003,3), (2001,2003)(2001,2003); how many times can Ayse guarantee to win?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4