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.

	Select Click for Answer
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?

	Select Click for Answer
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.

	Select Click for Answer
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.

	Select Click for Answer
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?

	Select Click for Answer
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.

	Select Click for Answer
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.

Click for Answer

October 26, 2021October 25, 2021 | Puzzles

“The Frogs and Tumblers”

A puzzle by Henry Dudeney. Frogs sit on eight of these 64 tumblers so that no two occupy the same row, column, or diagonal. “The puzzle is this. Three of the frogs are supposed to jump from their present position to three vacant glasses, so that in their new relative positions still no two frogs shall be in a line. What are the jumps made?” The frogs may not exchange positions; each must jump to a glass that was not previously occupied.

(“But surely there must be scores of solutions?” “I shall be very glad if you can find them. I only know of one — or rather two, counting a reversal, which occurs in consequence of the position being symmetrical.”)

	Select Click for Answer
“The frogs that jump are George in the third horizontal row; Chang, the artful-looking batrachian at the end of the fourth row; and Wilhelmina, the fair creature in the seventh row. George jumps downwards to the second tumbler in the seventh row; Chang, who can only leap short distances in consequence of chronic rheumatism, removes somewhat unwillingly to the glass just above him — the eighth in the third row; while Wilhelmina, with all the sprightliness of her youth and sex, performs the very creditable saltatory feat of leaping to the fourth tumbler in the fourth row. In their new positions it will be found that of the eight frogs no two are in a line vertically, horizontally, or diagonally.” (Henry E. Dudeney, “The Professor’s Puzzles,” Strand 12:12 [December 1896], 720-726; “The Professor’s Puzzles: Solutions,” Strand 13:1 [January 1897], 106-109.)

Click for Answer

October 19, 2021October 18, 2021 | Puzzles