Problem
COM-B1-M08-P012 A \(4\times6\) Chocolate Bar
#12
★★☆☆☆ Level 2 of 5
Players alternately break one existing rectangular piece of a \(4\times6\) chocolate bar along a grid line into two rectangles. A player who cannot move loses. Who wins?
Each move increases the number of pieces by \(1\).
Initially there is \(1\) piece, and at the end there must be \(24\) unit squares. Each move increases the number of pieces by exactly \(1\). Therefore there are \(24-1=23\) moves. The odd-numbered last move is made by the first player, so the first player wins.
A game where the number of moves is invariant.