The Mathematical Craze of the Crossword

In 1924, a new craze swept America. This was not of the same kind as the dance marathons, flagpole sitting and goldfish-eating competitions that gained popularity during this period. No, this was a much less lively pastime. After last week’s post about the Rubik’s Cube, it’s time to move on to a new type of puzzle – the crossword.

Indeed, the New York Times noted the craze of the crossword with alarm, calling it a “sinful waste in the utterly futile finding of words the letters of which will fit into a prearranged pattern, more or less complex.” However, since then, crosswords have become an important part of the daily lives of many not only in the US, but also in the UK. Indeed, a new type of crossword has sprung up which provides another dimension to the puzzle – the cryptic.

Here is an example of a cryptic crossword clue:


On the surface, this idea seems ridiculous. However, the aim is to correctly deconstruct the clue so as to find two separate clues, which both give the same answer:


Clue 2: FISH

Now our task seems much simpler. We need to find the name of a fish, which is also something which birds sit on. The answer, in this case, is PERCH. From what seemed a difficult task, a clear answer has been obtained.

The above clue needed to be split into two parts in order to be solved – however, this is not the only kind of cryptic clue. Indeed, there are many different rules to follow and different types of clue to consider when solving such a crossword, including anagrams, double-meaning clues and hidden words. The mark of a good clue is often the cleverness of the interpretation required to move from its ‘surface’ (the idea immediately suggested by the clue, such as a bird sitting on a fish in the above example) to its solution.

An interesting aspect of cryptic crosswords is that the people who like to solve them are often not linguists or authors, but scientists and mathematicians. Those from mathematical and IT backgrounds are particularly good at solving these kinds of crosswords, which require the correct deconstruction of difficult clues.

What is it about these puzzles that attracts numerical minds? I have a few ideas. The first is that these crosswords require a certain kind of creative, out-of-the-box way of thinking. It is this kind of thinking that leads to new theories and the solutions of new mathematical problems. There is also a similarity between crossword clues and algebraic expressions. Both have a set of ‘terms’ which change and interact with one another in some way, providing a final ‘solution’. The only real difference is that crossword clues can be interpreted in many different ways, and a certain word or punctuation mark does not always produce the same effect. Mathematicians, unlike crossword solvers, do not spend hours trying to figure out the correct ‘interpretation’ of an algebraic expression – there is only one correct way of looking at it.

I also think it might be related to the ‘penny-drop’ moment when a solver finally comes to the answer of a difficult clue. Personally, it is this satisfaction at the end of a difficult problem that attracts me to both mathematics and crosswords. And I suspect that this is the same for many others.

Moreover, with crosswords as with mathematics, there’s a set of rules to follow – but, like in maths, it isn’t enough just to know these rules. You have to be able to apply them in new situations. This might be the fundamental difference between mathematicians and linguists in terms of their crossword-solving capabilities – language is full of oddities and exceptions that simply do not occur in the mathematical world. A mathematician’s brain is trained to apply rules, a skill which a blank crossword gives it ample opportunity to use.