Use your wits! Can you solve these fiendishly difficult puzzles?

Isn't it time we learned to reconnect with the idea of problem-solving for fun? After all, argues Alex Bellos, the best puzzles are pieces of poetry. In an exclusive extract from his new book, he selects some of his favourites
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For those of us whose school memories include struggling with long division and quadratic equations, it may be surprising to learn that there was a time when almost all mathematics was recreational.

In the medieval world, for example, the role of maths was mostly as an intellectual diversion. (Apart from its use for technical, real-life tasks like measuring land area or calculating tax.) When, in 799, the British scholar Alcuin of York sent a letter containing 50 or so maths problems to Charlemagne, he did so not to infuriate the king but to amuse him.