Monthly Archives: July 2015

Puzzle #7: Gridlock


A quick puzzle to keep things ticking over until the imminent return of the Mad Hatter. Suitable for A-level students and top-end GCSE, or even KS3. Has been known to stump maths teachers too:

#7: Gridlock
A deceptively simple puzzle. Fill in the grid.
Published: 29/07/2015
Difficulty: *
Maths knowledge required: Very basic – calculating means.

The solution will be available next week.

IMAGE: – Creative Commons

The giant crab that I have chosen to illustrate this post is not relevant to the puzzle, but bonus points go to anyone who knows why I have picked it and can provide an appropriate response… Continue reading

No, the answer wasn’t obvious…

Squares Puzzle Stephen Morris has provided a very detailed response to this question, which I have copied to the end of the original post.

It turns out that my intuition was correct (the tiling is possible if and only if r is a rational number lying in the half open interval (0,1]), but the proof is not obvious. The maths involved seems to be rather lovely though, so Stephen’s comments are well worth a look.