# 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.

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.

In ancient times, too, many arithmetical problems were designed to entertain. Indeed, for the Greeks, a principle motivation for studying geometry was intellectual stimulation and discovery, with no concern for practical applications.

Maths got serious during the scientific revolution. Blame Isaac Newton. The discovery of his laws of motion and gravitation and the infinitesimal calculus, which provided the tools for dealing with these new ideas created new, difficult jobs for mathematicians to do, like finding the equations that describe as much of the world as possible.

The consequences are still felt today. Maths has mostly lost its reputation as a vehicle for playfulness and diversion. (When a piece of mathematics becomes successful, as in the case of sudoku, people make the excuse that this isnt maths, as if it stops being so merely by being popular.) And this is a shame, because we are depriving ourselves of a lot of fun.

Maths and logic puzzles are pleasurable and life-affirming because they force us to use our wits. A good puzzle is also never too hard to solve, thus presenting us with an achievable goal, supremely gratifying when it comes. In a puzzle we are proving to ourselves that we can do something we doubted we could. Deductive reasoning in simple logical steps is comforting, especially when real life is so illogical.

Beginning with Alcuin, Britain has produced many illustrious puzzlesmiths. Alcuin is notable as the first writer to introduce humour into mathematical problems, and his teasers have stood the test of time. Few adults can be unaware of his most famous riddle, about a traveller trying to cross a river with a wolf, a goat and some cabbages, which was once even featured in an episode of The Simpsons. I like the other types of puzzle he introduced too, such as questions about strange family relationships.

In the 19th century Lewis Carroll popularised the fun to be had with logic in Alices Adventures in Wonderland and Through the Looking-Glass. But Britains greatest ever puzzle inventor was Henry Ernest Dudeney, whose puzzles appeared for decades in British newspapers and magazines. In April 1930, the month Dudeney died, one of his most influential puzzles appeared in Strand Magazine the literary journal that published Conan Doyles first Sherlock Holmes stories. Smith, Jones and Robinson inspired a whole new genre of inferential logic puzzles in which the solver must deduce conclusions from a list of whimsical statements. These puzzles invite you to become a detective. On first reading it looks like there is far too little information to find the answer. But slowly you will piece together the clues.

Even when maths got serious in the late 17th century, however, it did not totally lose its element of play. As well as finding out the equations for commonplace phenomena like the vibration of string, mathematicians also used Newtons new tools to investigate unusual and bizarre curves. In fact, many great discoveries have come from mathematicians trying to understand simple puzzles and games. Most obviously, perhaps, the field of probability and therefore all of statistics was the result of Blaise Pascal and Pierre de Fermats correspondence about gambling games.

Not only have great mathematicians used simple brainteasers to inspire new research, but they have also devised many of their own puzzles. Edouard Lucas, who in the 19th century made important advances in our understanding of prime numbers, wrote a book of puzzles for the general reader and also invented a few classic problems.

Despite the current poor image of maths, the ubiquity of sudoku attests that maths puzzles do remain a popular pastime for many. I discovered quite how much a good puzzle can go viral when I posted a puzzle from a Singapore maths exam on my Guardian puzzle blog: the post was the ninth most read story across the Guardian online for last year, and the post with the solution was the sixth. The success of that puzzle inspired me to delve into puzzle history and rediscover many puzzles from the last thousand years. One of my favourites is only a few decades old, from the Japanese puzzle maven Nob Yoshigahara.

The best puzzles, like this one, are pieces of poetry. With elegance and brevity they pique our interest, kindle our competitive spirit, and in some cases reveal universal truths. Puzzles appeal to our impulse to make sense of the world, but most importantly they indulge our intellectual playfulness. Yet no matter how frivolous or contrived they are, the strategies we use to solve them expand our armoury for tackling other challenges in life.

Ever since the birth of mathematics, we have enjoyed posing and answering puzzles. And long may we continue to do so.

## Puzzle 1: qwerty

The 10 letter keys on the top line of a typewriter are
Q W E R T Y U I O P
Can you find a 10-letter word that uses only these keys?