Nick’s Mathematical Puzzles

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Welcome to my selection of mathematical puzzles. I aim to add one new puzzle each week, so please stop by again.

What’s new? See puzzle 160.

The math puzzles presented here are selected for the deceptive simplicity of their statement, or the elegance of their solution. They range over geometry, probability, number theory, algebra, calculus, trigonometry, and logic. All require a certain ingenuity, but usually only pre-college math. Some puzzles are original.

Explaining how an answer is arrived at is more important than the answer itself. To this end, hints, answers, and fully worked solutions are provided, together with links to related mathematical topics. Further references are provided with many of the solutions. The puzzles are intended to be fun, with an educational element.

Each puzzle is assigned a level of difficulty of between one and four stars, with four being the most difficult. Clearly this is to some extent subjective, but it may be useful as a rough guide.

The source for each problem is given at the bottom of the solution page. I usually provide only a proximate credit; some math puzzles have been around for so long it can be difficult to trace their provenance. However, if I know the original source, such as when a puzzle is a recognized mathematical theorem, I credit that source.

I welcome feedback of any kind. Should you find a puzzle ambiguous, a hint misleading, an answer incorrect, or a solution unclear, please let me know. I also welcome new math puzzles.

Some brief biographical information. I gained a maths degree from a British university in the 1980s. I’ve worked in computer software since then, but I retain a keen interest in mathematics and in education.

Reprinted with permission from Nick’s Mathematical Miscellany.

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