In this 2 x 2 grid pebble game, the player with the winning strategy is the one who goes first, given that they follow the optimal strategy.
Let’s denote the players as Player 1 and Player 2.
Here’s the optimal strategy for Player 1:
In the first turn, Player 1 should remove only one pebble.
Now there are three pebbles left on the grid. Player 2 has two choices:
a. Remove one pebble, leaving two pebbles behind.
b. Remove two nearby pebbles, leaving one pebble behind.
Regardless of Player 2′s choice, Player 1 can now remove the remaining pebbles in their next turn and win the game.
By following this strategy, Player 1 will always win the game, regardless of what moves Player 2 makes
Solves it fine now:
In this 2 x 2 grid pebble game, the player with the winning strategy is the one who goes first, given that they follow the optimal strategy.
Let’s denote the players as Player 1 and Player 2.
Here’s the optimal strategy for Player 1:
In the first turn, Player 1 should remove only one pebble. Now there are three pebbles left on the grid. Player 2 has two choices: a. Remove one pebble, leaving two pebbles behind. b. Remove two nearby pebbles, leaving one pebble behind. Regardless of Player 2′s choice, Player 1 can now remove the remaining pebbles in their next turn and win the game. By following this strategy, Player 1 will always win the game, regardless of what moves Player 2 makes