A Rolling Lemon

https://pixabay.com/en/meter-the-speedometer-6-800-miles-1088413/

My lousy car has an odometer without 4s — in every position, the counter advances from 3 directly to 5. For example, when it read 000039 I drove one mile and watched it roll over to 000050. Today the odometer reads 002005. How many miles has the car actually traveled?

Click for Answer

Left or Right?

bicycle puzzle

You come upon the track of a bicycle in the mud. Was the bicycle traveling to the left or the right?

Click for Answer

Pagan Island

https://pixabay.com/en/island-beach-ocean-water-boat-997022/

Twenty-six villages are ranged around the coastline of an island. Their names, in order, are A, B, C, …, Z. At various times in its history, the island has been visited by 26 missionaries, who names are also A, B, C, …, Z. Each missionary landed first at the village that bore his name and began his work there. Each village was pagan to begin with but became converted when visited by a missionary. Whenever a missionary converted a village he would move along the coastline to the next village in the cycle ABC-…-ZA. If a missionary arrived at an uncoverted village he’d convert it and continue along the cycle, but there was never more than one missionary in a village at a time. If a missionary arrived at a village that had already been converted, the villagers, feeling oppressed, would kill him and revert to a state of paganism; they would do this even to a missionary who had converted them himself and then traveled all the way around the island. There’s no restriction as to how many missionaries can be on the island at any given time. After all 26 missionaries have come and gone, how many villages remain converted?

Click for Answer

The Barbershop Paradox

https://commons.wikimedia.org/wiki/File:Barbier_par_Brispot.jpg

In 1894 Lewis Carroll published a conundrum that, he wrote, presents “a very real difficulty in the Theory of Hypotheticals.” Suppose that Allen, Brown, and Carr run a shop. At least one of them must always be present to mind the shop, and whenever Allen leaves he always takes Brown with him. Now, suppose that Carr is out. In that case then if Allen is out then Brown must be in, in order to tend the shop. But we know that this isn’t true — we’ve been told that whenever Allen is out then Brown is out.

Since the supposition that Carr is out leads to a falsehood, then it must itself be false. Confusingly, the laws of logic seem to require that Carr never leave the shop.

“I greatly hope that some of the readers of Mind who take an interest in logic will assist in clearing up these curious difficulties,” Carroll wrote. Modern logicians would say that this is a simple error in reasoning, rather than a logical disaster. But what is the error?

Click for Answer

The Falling Chain

Here are two identical rope ladders with slanting rungs. One falls to the floor, the other onto a table. The ladders are released at the same time and fall freely, but the one on the left falls faster, as if the table is “sucking” it downward. Why does this happen?

Click for Answer

Podcast Episode 100: Lateral Thinking Puzzles

https://commons.wikimedia.org/wiki/File:Mono_pensador.jpg

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.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

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:

Hotel: Listener Paul Sophocleous

Train: Listener Sean Gilbertson

Safe (more information): Listener David White

Robber (more information): Sharon Ross

Murder: Paul Sloane and Des MacHale, Intriguing Lateral Thinking Puzzles, 1996

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

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

Perspective

perspective puzzle

AB and CD are consecutive ties across a pair of railroad tracks that appear to meet at O on the horizon, H. If the ties are parallel to the horizon and are equally spaced along the tracks, how can we draw the next tie in this perspective figure?

Click for Answer

Black and White

spencer chess problem

G.B. Spencer devised this ingenious diagram in 1906: It contains 16 separate chess problems, one on each rank and file. In each case, ignore the pieces not on that rank or file and find a way for White to mate in two moves.

For example, the solution to the problem on the first rank is 1. Bd4 Ke2 2. Ng3#. What are the other 15 solutions?

Click for Answer