Podcast Episode 152: Lateral Thinking Puzzles


Here are five new lateral thinking puzzles to test your wits and stump your friends — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

Here are the sources for this week’s puzzles. In a couple of places we’ve included links to further information — these contain spoilers, so don’t click until you’ve listened to the episode:

Puzzle #1 was contributed by listener Dave Lawrence.

Puzzle #2 is from listener Michael Berman.

Puzzle #3 is from Paul Sloane and Des MacHale’s Ingenious Lateral Thinking Puzzles, 1998.

Puzzle #4 is from listener Paul Sophocleous. Here are two associated links.

Puzzle #5 is from listener Noah Kurland. Here’s an associated link.

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at http://feedpress.me/futilitycloset.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, 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!

In a Word

n. the amount a container lacks of being full

Given a 5-gallon jug, a 3-gallon jug, and a limitless supply of water, how can you measure out exactly 4 gallons?

Click for Answer

The Cherries Puzzle

ozanam cherries puzzle

A classic puzzle from Jacques Ozanam’s Recreations Mathematiques et Physiques, 1723. Two slits (CD) and two holes (EF) are cut in a slip of paper, and a cherry stem is suspended as shown. The cherries are too large to fit through the holes. How can you free the stem and its cherries intact from the slip?

Click for Answer

Cross Purposes

Three men, A, B, and C, are given a test in quick thinking. Each man’s forehead is marked with either a blue or a white cross, and they’re put into an empty room. None of the three can see the color of his own cross, and they aren’t allowed to communicate in any way. Each is told that he can leave the room if he either sees two white crosses or can correctly deduce the color of his own cross.

The men know each other well, and A knows he’s just a bit more alert than the others. He sees that both B and C have blue crosses, and after a moment’s thought he’s able to leave the room, having correctly named the color of his own cross. What was the color, and how did he deduce it?

Click for Answer

77777 …

A curious puzzle from the Penguin Problems Book, 1940:

A certain number consisting entirely of 7s is divisible by 199. Find the last four digits of the quotient, without finding the entire quotient.

Click for Answer

A Hat Puzzle

khovanova hats

A puzzle by MIT mathematician Tanya Khovanova:

Three logicians walk into a bar. Each is wearing a hat that’s either red or blue. Each logician knows that the hats were drawn from a set of three red and two blue hats; she doesn’t know the color of her own hat but can see those of her companions.

The waiter asks, “Do you know the color of your own hat?”

The first logician answers, “I do not know.”

The second logician answers, “I do not know.”

The third logician answers, “Yes.”

What is the color of the third logician’s hat?

Click for Answer