There are two piles of pebbles. Each pile contains 7 pebbles. Each player can pick as many pebbles they want from either of the piles. The player who picks the last pebble wins. Try this game with your friends. Now, how do you play so that you win?
Winning Strategy: A player should aim to leave equal numbers of pebbles in both piles after their turn.
Key Insight: If both piles have the same number of pebbles, the opponent is in a losing position.
How to Play:
- If you start and both piles have 7 pebbles each, let your opponent go first.
- Whatever they take from one pile, you take the same amount from the other pile.
- This keeps the piles equal after every move.
- Eventually, you will take the last pebble.
∴ The winning strategy is to always mirror your opponent's moves on the opposite pile to maintain equal piles.
Explanation
This is a mathematical game strategy problem. The key insight is that equal piles represent a losing position for the player whose turn it is. If you can always leave equal piles for your opponent, you will win. The strategy involves mirroring your opponent's moves on the opposite pile.
Solution Steps
Identify that equal piles represent a losing position for the player whose turn it is.
If starting with equal piles (7 pebbles each), let your opponent go first.
Whatever amount your opponent takes from one pile, take the same amount from the other pile.
Continue mirroring moves to keep piles equal after each of your turns.
You will eventually take the last pebble and win.