This week's poser: The Magic Rectangle

A mind-boggling conundrum that will test you to the limit. Well, maybe not...

Once upon a time, when I was still at school, someone brought in a curious book (or were we still using scrolls back then?). It was a sort of miscellany, full of strange facts, unsolved mysteries and accounts of vaguely paranormal phenomena. Sadly neither the title of the book nor the name of its author remain in the memory banks. I can’t remember any of its contents either, except one: a puzzle I have christened The Magic Rectangle.


It started off with an illustration of a pretty ordinary-looking rectangle divided into squares. The following is purely from memory and therefore unlikely to match the original:

You were then shown how to divide the rectangle up into a number of smaller shapes. Again this is only a notional example, done purely from memory:

The next step was to cut the rectangle up and rearrange the shapes to form a big square. So far so good. But when you’d done this and counted up all the little squares forming the new shape, one of them was missing!


I know this sounds silly and is clearly impossible, but that’s how I remember it. Can anyone shed any light on the matter- either the identity of the book or a solution to the problem? And does anyone know of any similar puzzles? Remember, the fate of nations could be at stake...