Brain Teasers
Knight's Trouble
Having failed to achieve his previous goal, the knight wanted to leave Breadland. However, he was captured by the king of Breadland for stepping all around in his kingdom.
The king decided to sentence the knight to death, but before that he wanted to test the knight's intelligence. The king said:
"Play a game of chess with me. You know, in my kingdom, the chessboard is 9x7. Each player has a queen on each side of the king, one is next to the king and the other is between a bishop and a knight. Also, each player has an additional pawn.
But this time the rule is changed. Each player in turn must make TWO legal moves. He can't put his king in check either after his first move or after his second move.
If you win or the game ties, I'll set you free. If I win, I'll sentence you to death immediately.
You move first."
Could the knight avoid being sentenced to death?
The king decided to sentence the knight to death, but before that he wanted to test the knight's intelligence. The king said:
"Play a game of chess with me. You know, in my kingdom, the chessboard is 9x7. Each player has a queen on each side of the king, one is next to the king and the other is between a bishop and a knight. Also, each player has an additional pawn.
But this time the rule is changed. Each player in turn must make TWO legal moves. He can't put his king in check either after his first move or after his second move.
If you win or the game ties, I'll set you free. If I win, I'll sentence you to death immediately.
You move first."
Could the knight avoid being sentenced to death?
Hint
I only asked whether or not the knight could avoid being sentenced. I didn't ask which moves must the knight make to avoid being sentenced.Answer
The answer is affirmative.Assume that the knight couldn't avoid being sentenced. This means that no matter what moves the knight made, the king could always win.
Then the knight could move one of his knights and then move back.
But then every piece would be on its original position, and it would be the king's turn to move, and the knight could win the game, which contradicts our assumption.
Hence, the knight had a strategy to guarantee at least a tie.
Note that I didn't point out what the strategy is. I only showed its existence.
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