Problem
COM-B1-M08-P004 Two Equal Piles
#4
★☆☆☆☆ Level 1 of 5
There are two piles of \(10\) stones each. In one move, a player may take any positive number of stones from one pile. The last move wins. Prove that the second player wins.
The second player copies the move in the other pile.
After each first-player move, the second player takes the same number of stones from the other pile. Thus after the second player’s move the piles are equal again. If the first player could take stones from one pile, the other pile had the same number of stones, so the response is legal. Hence the second player will not run out of moves before the first and will make the last move.
First pairing strategy in pile games.