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Category Archives: Puzzles
Solution to the conversionkicking problem
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
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Puzzle: kicking the conversion
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
Solution to the summing problem
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
A summing problem
Here’s a nice little problem that somebody brought along to the Skills Centre recently. (Thanks to Dr Peter Davidson for the tipoff!) We define for natural numbers . The task is to prove that . As so often, there’s an … Continue reading
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Solution to Joyner’s five statements problem
Recall this problem from David Joyner’s book Adventures in Group Theory:
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Puzzle: Joyner’s five statements
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
Solution: game, set and mismatch
For those of you who’ve not worked it out, here’s the explanation of that apparent paradox in the tennis match statistics.
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