Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.
Are you here to participate in a specific proposal? Click on the proposal tag (with the dark outline) to see only posts about that proposal and not all of the others that are in progress. Tags are at the bottom of each post.
Mutilated chessboard problem Question
This post describes a classic puzzle.
If you have previously seen this puzzle I request that you allow someone else to solve it and post their answer.
Thank you!
Mutilated chessboard problem:
2 corner squares of a chessboard have been cut out as shown below.
You have 31 dominoes each of which can exactly cover two adjacent squares in the chessboard.
Can you completely cover every square of the mutilated chessboard with the 31 dominoes?
Attribution:
Max Black in his book Critical Thinking (1946)
1 answer
Answer! Click here to reveal
It is not possible to completely cover every square of the mutilated chessboard with the 31 dominoes.
Details! Click here to reveal
Every domino whether placed horizontally or vertically will cover exactly one black square and one red square. So 31 dominoes would cover 31 black squares and 31 red squares.
But the mutilated chessboard has 32 black squares and 30 red squares. Therefore the covering is not possible.
There is a Wikipedia article about this puzzle:
0 comment threads
0 comment threads