Earlier today, I set this puzzle:
Is it possible to cover an 8x8 chessboard with 32 dominos (which are each a 1x2 block) in such a way that any line parallel to a side of the chessboard always passes through the interior of at least one of the dominoes?
If it is possible, draw an example. If it isn’t, prove it.
(Each domino is a 1x2 rectangle, which means that each domino will cover two adjacent squares perfectly. The dominoes must cover the board completely, which means lie flat on the squares leaving no gaps nor overlaps.)
I also suggested that you start off by trying to solve the same problem with a 4x4 board and a 6x6 board .
Yes, it is possible. And many of you sent me your solutions. Here’s one:
And another, this time with left-right symmetry. (The space invader solution)
And here’s another, with rotational symmetry.
The reason that I encouraged you to try with 4x4 and 6x6 boards is that it is impossible when the boards are this size. The smallest board which it is possible is the 8x8.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of several books of popular maths and puzzles, most recently an updated, 10th anniversary edition, of Alex’s Adventures in Numberland.
Thanks to Carlos D’Andrea of the University of Barcelona for suggesting this puzzle.