A Simple Plan

https://commons.wikimedia.org/wiki/File:Cuboid_abcd.svg — Image: Wikimedia Commons

You have three identical bricks and a ruler. How can you determine the length of a brick’s interior diagonal without any calculation?

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Stack two of the bricks and place the third alongside. Now you’ve identified the corners of an invisible fourth brick, whose diagonal you can measure directly with the ruler. (Bonus: If the bricks’ edges and face diagonals all have integer lengths, and you find that the interior diagonal is an integer as well, you’ll have solved an open problem in mathematics.) 01/03/2021 UPDATE: Reader Paul-Georg Becker points out that the task can be accomplished with two bricks and a ruler: (Thanks, Paul-Georg.)

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January 3, 2022January 3, 2022 | Puzzles · Science & Math

RSS Quiz

The Royal Statistical Society has released its Christmas quiz for 2021, a set of 11 puzzles that require general knowledge, logic, lateral thinking, and searching skills, but no specialist mathematical knowledge.

Anyone may enter, individually or in teams of up to five. The top entry will receive £150 in Wiley book vouchers, second place £50 in book vouchers, and the next three entries a puzzle book or board game. And everyone who achieves a score of 50 percent or higher will win a donation to their favorite charity or good cause.

Entries must be received by 21:00 GMT on January 31. See the quiz web page for the rules and some tips for budding solvers.

December 25, 2021 | Puzzles

A Christmas Puzzle

Mathematician Matthew Scroggs has released this year’s Christmas card for Chalkdust magazine. (Actually I’m late — it’s been out since December 4.)

Solving 14 puzzles will reveal a Christmas-themed picture in this diagram.

You can download the card as a PDF or complete it online.

December 22, 2021December 21, 2021 | Puzzles

Black and White

taylor chess problem

By J. Paul Taylor. White to mate in two moves.

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1. Nc4! and the queen will mate. From Elementary Chess Problems, 1880.

December 20, 2021December 19, 2021 | Puzzles

Crowd Control

A knight’s tour is a series of moves by a chess knight such that it visits each square on the chessboard once. The example above is a “closed” tour because it ends on the square where it started.

This inspired a puzzle posed by Martin Gardner. If we filled a standard chessboard with knights, one on each square, could all 64 of them move simultaneously? The closed knight’s tour shows that they could — they form a long conga line, with each knight vacating a square for the knight behind it to occupy.

Gardner asks: Could the same feat be accomplished on a 5 × 5 chessboard?

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The answer is no, and we can prove it by observing the board’s coloring. A 5 × 5 chessboard has 13 squares of one color and 12 of another. The nature of a knight’s move means that it always jumps from a square of one color to a square of another. So on a 5 × 5 chessboard, 13 knights would have to jump onto 12 squares, which is impossible. So the task can’t be done.

December 15, 2021December 14, 2021 | Puzzles

Podcast Episode 365: Lateral Thinking Puzzles

For this final episode of the Futility Closet podcast we have eight new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

Intro:

Sears used to sell houses by mail.

Many of Lewis Carroll’s characters were suggested by fireplace tiles in his Oxford study.

The sources for this week’s puzzles are below. In some cases we’ve included links to further information — these contain spoilers, so don’t click until you’ve listened to the episode:

Puzzle #1 is from Greg. Here are two links.

Puzzle #2 is from listener Diccon Hyatt, who sent this link.

Puzzle #3 is from listener Derek Christie, who sent this link.

Puzzle #4 is from listener Reuben van Selm.

Puzzle #5 is from listener Andy Brice.

Puzzle #6 is from listener Anne Joroch, who sent this link.

Puzzle #7 is from listener Steve Carter and his wife, Ami, inspired by an item in Jim Steinmeyer’s 2006 book The Glorious Deception.

Puzzle #8 is from Agnes Rogers’ 1953 book How Come? A Book of Riddles, sent to us by listener Jon Jerome.

You can listen using the player above, download this episode directly, or subscribe on Google Podcasts, on Apple Podcasts, or via the RSS feed at https://futilitycloset.libsyn.com/rss.

Many thanks to Doug Ross for providing the music for this whole ridiculous enterprise, and for being my brother.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

November 29, 2021November 28, 2021 | Podcast · Puzzles

Black and White

kling chess problem

By Joseph Kling. White to mate in two moves.

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1. Re6! forces the black king to move to f1, when 2. Rf3 is mate. From The Chess Euclid, 1849.

November 26, 2021November 25, 2021 | Puzzles

Black and White

bull chess problem

By T.P. Bull. White to mate in two moves.

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1. Qd8! and the queen will mate. From Bull’s Chess Problems, via Charles F. Wadworth, Unique Chess Problems, 1890.

November 4, 2021November 28, 2021 | Puzzles

“The Hammock Puzzle”

By Sam Loyd. What’s the least number of cords you’d have to cut to divide this hammock into two pieces?

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Twelve: From Loyd’s Cyclopedia of Puzzles, 1914.

October 27, 2021October 26, 2021 | Puzzles

Exercise

https://commons.wikimedia.org/wiki/File:Euclid_Tetrahedron_4.svg — Image: Wikimedia Commons

A problem from Peter Winkler’s excellent collection Mathematical Puzzles, 2021:

Four bugs live on the four vertices of a regular tetrahedron. One day each bug decides to go for a little walk on the tetrahedron’s surface. After the walk, two of the bugs have returned to their homes, but the other two find that they have switched vertices. Prove that there was some moment when all four bugs lay on the same plane.

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Call the bugs A, B, C, and D. In the initial position, when D looks at the other three bugs, she sees triangle ABC labeled clockwise, but in the final position she sees it labeled counterclockwise (or vice versa). Since the bugs move continuously, some position must arise during the walk in which either D is on the plane ABC or ABC do not determine a plane. In the latter case they’re collinear, which means they share a plane with any other point, including D.

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October 26, 2021October 25, 2021 | Puzzles