MathDB
Player who takes the last match wins

Source: Baltic Way 2010

November 19, 2010
combinatorics proposedcombinatorics

Problem Statement

There is a pile of 10001000 matches. Two players each take turns and can take 11 to 55 matches. It is also allowed at most 1010 times during the whole game to take 66 matches, for example 77 exceptional moves can be done by the first player and 33 moves by the second and then no more exceptional moves are allowed. Whoever takes the last match wins. Determine which player has a winning strategy.