Category Archives: Puzzles

Remember Regiomontanus’s rugby problem? Expressed in geometrical terms, the task was this: given two points A and B (the goalposts) and a third point T (the location of the try) lying on the same straight line, find a point P … Continue reading →

In honour of the Six Nations rugby tournament currently taking place, here’s a problem in plane geometry loosely inspired by one of the many dilemmas facing a rugby player. For those unfortunate enough not to be familiar with the sport: … Continue reading →

Remember that wee summing problem we introduced last week? The task was to prove that , where . How you prefer to tackle problems like this will depend on your mathematical “personality” and on the tools you have available. For … Continue reading →

Here’s a nice little problem that somebody brought along to the Skills Centre recently. (Thanks to Dr Peter Davidson for the tip-off!) We define for natural numbers . The task is to prove that . As so often, there’s an … Continue reading →

Recall this problem from David Joyner’s book Adventures in Group Theory:

The following little logical teaser appears as “Ponderable 1.1.3” in David Joyner’s book Adventures in Group Theory (Johns Hopkins University Press, 2008; also available to download for free). Determine which of the following statements is true. Exactly one of these … Continue reading →

For those of you who’ve not worked it out, here’s the explanation of that apparent paradox in the tennis match statistics.

I turned on the TV this weekend in the middle of the Wimbledon coverage. The second set of a match had just finished, and they were displaying a page full of statistics for the two players’ performances. I can’t remember … Continue reading →

The puzzle was to show that a cube cannot be dissected into a finite number of smaller cubes, all of different sizes. Here’s a slightly expanded version of the proof given in Littlewood’s Miscellany. The approach, as with many impossibility … Continue reading →

This puzzle comes from the first chapter of Littlewood’s Miscellany (J. E. Littlewood, ed. B. Bolobás, CUP, 1986), which is entitled “Mathematics with minimum ‘raw materials’”. Littlewood quotes a very neat solution which is worth trying to discover for yourself… … Continue reading →