We’re giving out apples to a group of boys. If we distribute the entire supply, then every boy will get three, except for one, who will get two. If instead we give each boy two apples, then we’ll have eight apples left over. How many apples are there altogether?

# Puzzles

# Podcast Episode 353: Lateral Thinking Puzzles

Here are six new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

Intro:

Lili McGrath’s 1915 “floor polisher” is a pair of slippers connected by a cord.

Eighteenth-century English landowners commissioned custom ruins.

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 listener Moxie LaBouche.

Puzzle #2 is from listener Cheryl Jensen, who sent this link.

Puzzle #3 is from listener Theodore Warner. Here’s a link.

Puzzle #4 is from listener David Morgan.

Puzzle #5 is from listener Bryan Ford, who sent these links.

Puzzle #6 is from listener John Rusk, who sent this link.

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.

Please consider becoming a patron of Futility Closet — you can choose the amount you want to pledge, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

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

# Skulduggery

This secret message appears in J.J. Connington’s 1933 novel *Tom Tiddler’s Island*:

TEIIL LFILH TCETU FDHSO OENPR YYUGO HNGOF

LOVTU GCHAN NOATN AEHAT ISUWE ETFST GSCAD

OFRGH PELPE HASLE GASTH HGSMR LHLAR ARNIF

THRDL NITFO SSWSG NYILE EFALT ODECT IESOL

NTSNT COOUE AODNT IUTAI TIOON LEANR IIGOT

AHNOM FINHE YLMFD ATTTS MANHH OFEII ETODD

OTPCA MOTIE FMONG IMCLA TTCHB YIMNN ETROX

EMCOU VSFHE ELMPN NCTAW ETRWO OAHEE IYCNA

OIRBT RTXET PEIZN RSCSA TIKOH NITHT EMFNE

NNRUO GOTGP ENETP SYANS Z

What does it mean?

# Black and White

By Edith Baird. White to mate in two moves.

# Tank Hunt

A puzzle from Daniel J. Velleman and Stan Wagon’s excellent 2020 problem collection *Bicycle or Unicycle?*:

Before you is a field of 225 squares arranged in a 15×15 grid. One of the squares contains a perfectly camouflaged tank that you’re trying to destroy. You have a weapon that will destroy one square of the grid with each shot, but it takes two shots to destroy the tank, and you know that when the tank has been hit the first time (and only then) it will flee invisibly to an adjacent square (horizontally or vertically). What’s the minimum number of shots you’ll need to be sure of destroying it?

# The Wine-Bin

A puzzle by Claude Gaspar Bachet de Méziriac, from 1612, via Henry Dudeney:

A gentleman had a wine-bin of eight compartments, as in the illustration, containing 60 bottles, arranged as shown. His dishonest servant stole 4 bottles and rearranged the remainder. The gentleman noticed that the bottles had been redistributed, but as there were still 21 bottles on every side he innocently concluded that all the 60 were there. The servant, emboldened by his success, again stole 4 bottles and rearranged the remainder without discovery. In fact, on two more occasions he repeated his theft of 4 bottles, always leaving the remainder so arranged symmetrically that there were 21 on every side. How did he arrange them on the four occasions so as to steal the 16 bottles?

# Implementia

A puzzle by Yoshinao Katagiri: A boy and a girl played rock paper scissors 10 times. Altogether the boy played rock three times, scissors six times, and paper once, and the girl played rock twice, scissors four times, and paper four times (though, in each case, the order of these plays is unknown). There were no ties. Who won?

# Fixing a Point

A problem proposed by Richard Hoshino and Sarah McCurdy for *Crux Mathematicorum*, September 2008:

Five points lie on a line. Here are the 10 distances between pairs of points, listed from smallest to largest:

2, 4, 5, 7, 8, *k*, 13, 15, 17, 19

What’s *k*?

# Black and White

By E. Carney Jr. White to mate in two moves.

# Enlightenment

You’re in a dark room. The only light comes from an old LED digital alarm clock with four seven-segment displays. The time is displayed in 24-hour format, HH:MM (no seconds), and the leading digit is blank if not used. How much time passes between the room’s darkest state and its lightest?