Black and White

loquin chess problem

By François Paul Loquin. White to mate in two moves.

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1. Kf1! Kxh3 2. Bf5# From La Régence, 1849.

May 15, 2017May 28, 2017 | Puzzles

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.

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May 1, 2017September 30, 2017 | Podcast · Puzzles

Black and White

gottschall chess problem

By Hermann Von Gottschall. White to mate in two moves.

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1. Bh1! Kxh1 2. Rc1#

April 24, 2017May 7, 2017 | Puzzles

In a Word

ullage
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?

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Fill the 5-gallon jug and use it to fill the 3-gallon jug. That leaves 2 gallons in the 5-gallon jug. Empty the 3-gallon jug and transfer the 2 gallons from the 5-gallon jug to the 3-gallon jug. Fill the 5-gallon jug and use it to top off the 3-gallon jug. That requires exactly 1 gallon, leaving 4 gallons in the 5-gallon jug. You can also solve this geometrically, or you can let John McClane solve it for you: 04/23/2017 UPDATE: Two readers give a more efficient solution: Fill the 3-gallon jug and empty it into the 5-gallon jug. Fill the 3-gallon jug again and use it to top off the 5-gallon jug. This leaves 1 gallon in the 3-gallon jug. Empty the 5-gallon jug. Transfer the remaining gallon from the 3-gallon jug to the 5-gallon jug. Fill the 3-gallon jug again and pour it into the 5-gallon jug. This solution requires discarding 5 gallons altogether, where mine required discarding 6. (I think this is probably the alternate solution that Grossman’s method will obtain, but I haven’t had time to check.) (Thanks, Chris and Marty.)

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April 20, 2017April 30, 2017 | Language · Puzzles

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?

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Fold the slip and feed the strip through both holes as shown. Now you can draw one cherry through loop H.

April 14, 2017April 23, 2017 | Puzzles

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?

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His cross was blue. He thought, “If my cross were white, then B would see one blue and one white cross. In that event B would immediately know that his own cross could not be white, because if it were then C would see two white crosses and immediately leave the room. Similarly, if my cross were white then C would know that his own cross must be blue, since otherwise B would have gone out. Since neither B nor C has moved, my cross must be blue.”

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April 5, 2017April 16, 2017 | Puzzles

Black and White

de veer chess problem

By J.R.G. De Veer. White to mate in two moves.

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1. Qg3! Ke7 2. Qd6# From Jeugdproblem, 1914.

April 3, 2017April 16, 2017 | Puzzles

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.

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199 × the quotient equals the number we’re seeking (7777 …). Hence (200 × the quotient) minus the quotient will give us the same number. So let a, b, c, and d be the last four digits of the quotient. Now the quotient multiplied by 200 ends in r, s, 0, 0, where r, s are the digits that result from multiplying c, d by 2. Here’s the subtraction: So d must be 3, and c must be 2. Therefore s, which we know is twice d, is 6, and r, which is twice c, is 4. And that tells us that b is 8 and a is 6. So the last four digits of the quotient are 6823.

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April 2, 2017April 9, 2017 | Puzzles

Quickie

A puzzle by Frank Morgan: The meaning of a common English word becomes plural when an A is added at its start. What is the word?

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YES becomes AYES. From MIT Technology Review, July/August 2007.

March 29, 2017April 9, 2017 | Puzzles

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?

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If Logician #1 saw that both of her companions were wearing blue hats, then she’d know that her own hat must be red. But she says, “I do not know.” That tells us that either #2 or #3 (or both) is wearing a red hat. Logician #2 understands this. So if she saw that #3 was wearing a blue hat, then she’d know that she herself was wearing a red one. But she too says, “I do not know.” That means that Logician #3 must be wearing a red hat. Logician #3, realizing this, says so. Interestingly, Khovanova says her puzzle was inspired by a joke: Three logicians walk into a bar. The waitress asks, “Do you all want beer?” The first logician answers, “I do not know.” The second logician answers, “I do not know.” The third logician answers, “Yes.” She suggests that it might be valuable to find a way to convert jokes into puzzles and vice versa. (Tanya Khovanova, “Hat Puzzles,” Recreational Mathematics Magazine 1:2 [September 2014], 5-10.)

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March 28, 2017April 9, 2017 | Puzzles