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.


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!


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.

Click for Answer

“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.”)

Click for Answer


A memorable puzzle from the Russian science magazine Kvant:

How can a goat, a head of cabbage, two wolves, and a dog be transported across a river if it’s known that the wolf is ‘culinarily partial to’ goat and dog, the dog is ‘on bad terms with’ the goat, and the goat is ‘not indifferent to’ cabbage? There are only three seats in your boat, so you can take only two passengers — animal or vegetable — at a time.

(You can keep order within the boat.)

Click for Answer

Starting Funds


Three men play a game, agreeing that in each round the loser will double the money of each of the other two. After three rounds, each man has lost one time, and each man has $24. How much did each have at the start of the game?

Click for Answer

Black and White

gold chess problem

Henry Dudeney in Strand, June 1911: “It would be difficult to find a prettier little chess problem in three moves, produced from such limited material as a rook and a pawn, than the one given this month, by Dr. S. Gold. The novice will probably find the task of discovering the key move quite perplexing. White plays and checkmates in three moves.”

Click for Answer