In my opinion, it is increasingly rare to come across books of genuine rigour and originality when browsing the popular science section.
I should qualify the claim above by noting that these descriptions are subjective, and acknowledging such books are still published. For example, if one is searching for an original work then Hannah Fry’s Hello World is a thoughtful analysis of a contemporary issue, and Fermat’s Last Theorem by Simon Singh is both original in its depth, and high level in its content.
Although nowadays such new books are hard to find, from 1958 until 1997, Martin Gardner was a prolific author who regularly ticked both of these boxes. The Unexpected Hanging And Other Mathematical Diversions was first published in 1969, and for me stands out as especially good. Whilst the title might suggest a macabre theme, the content is actually an exploration of puzzles, paradoxes, and logical curiosities. The title is derived from the famous paradox of the unexpected hanging:
A man was sentenced to death by hanging on Saturday.
“The hanging will take place at noon,” said the judge to the prisoner, “on one of the seven days of the week, but you will not know which day it is until you are informed on the morning of the day of the hanging.”
When will the man be hanged?
The paradox lies in the inherent contradiction of the supposed surprise. If the prisoner were still alive on the final day of the week, they would inevitably know the hanging was imminent, contradicting the condition stated by the judge. The same reasoning would then apply recursively to the previous day, and so on. Whilst it is likely that some readers are familiar with this paradox, there are a wide variety of such puzzles within the book including some I tasked a small group of learners with at my first school.
At that school, I found myself hosting an informal chess club every lunchtime. Many of these learners were able mathematicians and high achievers more generally. I even saw one of this group captain a winning team on University Challenge recently! During the lunch hours, we explored some of the challenging chessboard puzzles found in The Unexpected Hanging, including those of the maximum attack, and the bishop and rook problem. These activities which were low floor, high ceiling and set in a context held in keen interest by the group. Consequently, they were also a huge success. I do often wonder how the learning experience could be enhanced if each of these criteria was met more often.
The challenging chessboard puzzles were excellent for a small, focused group but may not have been suitable for a larger class. Nevertheless, I have also used other chessboard puzzles from the book like the minimum attack problem, and the eight queens problem with larger groups. These were also successful, actively engaging the learners with strategy, and serving as a superior alternative to other more passive end of year activities.
In summary, Gardner’s The Unexpected Hanging remains a standout text for the recreational mathematician, and educators looking for engaging mathematical diversions! Have you read the book? Do you agree with my thoughts?
Another blog post, coming soon.
George Bowman
Founder, Maths Advance
MATHS ADVANCE BLOG 
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