Can you solve it? Domino dancing

A riddle about rectangles

UPDATE: To read solution click here

It’s a sin! Yes, I used a picture of the Pet Shop Boys to entrap you into reading my puzzle column. What did you do to deserve it?

Today’s poser (no, not him) concerns the playful positioning of domino-shaped tiles on a chessboard.

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.)

You might want to begin by trying to tile a 4x4 board with 8 dominos according to the constraints of the question, that is, such that any line parallel to a side always passes through the interior of at least one of the dominoes. Is this possible? Next, try with a 6x6 board and 18 dominoes. Are there any patterns?

I’ll be back at 5pm with the answer.

UPDATE: The solution can nw be read here.

PLEASE NO SPOILERS

If you happen to like tiling chessboards with dominoes, why not check out these two domino chessboard problems I set in this column in 2015.

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.

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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.

If you are reading this in the Guardian app, and you want a notification each time I post a puzzle, or its solution, click the ‘Follow Alex Bellos’ button above.

Contributor

Alex Bellos

The GuardianTramp

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