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A collection of puzzles

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Welcome to my selection of mathematical puzzles.

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.

Nick
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Nick Hobson
nickh@qbyte.org

Last updated: February 26, 2009

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Welcome to my selection of mathematical puzzles. 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.

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There is a great amount of satisfaction that can be obtained from solving a mathematical puzzle. There are many puzzles on this page, all with a mathematical connection, that are just waiting to be solved. You can earn Transum Trophies for the puzzles you solve.

The following puzzles are from the Transum monthly newsletters and podcasts.

The following puzzles are the Transum Advanced Starters.

Same Three Digits

Find ex pressions which contain indices and evaluate to numbers containing the same digits.

Advanced Starter

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An ever-growing collection of interactive mathematical and logic puzzles designed for anyone interested in school-level Maths.

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Lots of different styles including Kakuro, Sudoku and visual-spatial puzzles

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Printable puzzles. Thousands of 'em. All free.

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Hundreds of free Inky puzzles for printing.

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Here at Mental Floss, we love a good brain teaser-and clearly we're not alone. From cows and chickens to river crossings, we've never met a riddle we didn't want to solve-even if it was originally meant for a 5-year-old. The Bananas, Clock, Hexagon Viral Logic Puzzle, which math puzzle enthusiast Presh Talwalkar posted to his Mind Your Decisions blog, is the latest riddle to have us admittedly stumped.

According to Talwalkar, 99 percent of the people who attempt to solve the problem fail, leaving the remaining one percent to be dubbed geniuses for figuring it out. Which side will you land on?

"Solve If You Are A Genuis" - The Bananas, Clock, Hexagon Puzzle. The Correct Answer Explained. Blog: https://t.co/QEAp1Eflbf pic.twitter.com/yx8M8hsLVs
- Presh Talwalkar (@preshtalwalkar) March 9, 2017

The key to solving this puzzle is to look closely. We'll give you a minute to do just that (or you can start the video below-it will give you a little time before giving anything away).

Now it's time to come up with your answer. We'll give you another minute ...

So what did you come up with?

If you answered 38, congratulations-you might be a genius.

If you answered something else, don't worry, you're not alone.

Where most people seem to be going wrong with the problem is by not looking at the images closely enough when attempting to assign a numerical value. Specifically: In the last line of the problem, all of the images-the clock, the bananas, and the hexagon-are all slightly different than the images shown in the previous lines. If you noticed this, then you probably realized that the bunch of bananas in lines one, two, and three have a different value than the fruit seen on line four. Same goes for the clock and the hexagons. Which makes this as much a visual puzzle as it a math problem.

Finish watching the video above for Talwalkar's detailed explanation of how to solve the problem. Then stump your friends!

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The Math Puzzle That's Driving the Internet Bananas

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Here at Mental Floss, we love a good brain teaser-and clearly we're not alone. From cows and chickens to river crossings, we've never met a riddle we didn't want to solve-even if it was originally meant for a 5-year-old.

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Play solvemoji online

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Solvemoji - Emoji teaching resources - Emoji math puzzles, great as a primary math starter, download our pdf worksheets - great for home schooling

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Emoji based puzzles to print or use on screens

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Something went wrong, but don’t fret — let’s give it another shot.