Chessboard and Dominos | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Have you ever heard of the chessboard and dominos puzzle? It goes like this - there is an 8 by 8 chessboard with two diagonally opposite corners cut off. Can you use 31 dominos to cover the entire board?

The Initial Solution

At first glance, it seems like 31 dominos would be enough to cover the remaining 62 squares of the chessboard. After all, one domino can cover exactly two squares. But unfortunately, the answer is no.

Visualizing the Problem

To understand why it is impossible, let's visualize the problem. Each domino will always cover one black and one white square. Therefore, 31 dominos will cover 31 black squares and 31 white squares exactly. However, on this particular chessboard, we must have 32 black and 30 white squares (if we cut the corners with white squares), or 32 white and 30 black squares (if we cut the corners with black squares).

The Final Verdict

Hence, it is not possible to cover the entire board using only 31 dominos. This puzzle is known as an unsolvable problem.

Conclusion

This puzzle may seem straightforward at first, but it actually requires some critical thinking to solve. It is a great exercise for the brain and can help improve problem-solving skills. Next time you come across a problem that seems unsolvable, remember this puzzle and keep working at it until you find a solution.