Imagine a 10x10 chessboard with a fictitious King who can move in three possible directions: up, left and diagonally down-right,
- one step to adjacent square only.
Your task is to devise a route starting at a square of your choice and returning to the same square including in your itinerary each square of the board exacty once.
Present your solution or prove that it can't be done.
To make the tour of the 100 squares in a closed loop requires 100 moves. As each row and column must be visited the same number of times, and the King visits each one once on the way up and once on the way down (same for left and right column-wise), the number of up moves must equal the number of diagonal moves, but also the number of left moves must equal the number of diagonal moves.
So there are to be an equal number of each of the three types of move. But 100 is not divisible by 3, so the task is impossible.
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Posted by Charlie
on 2020-06-08 21:40:37 |
solution
