Prime Magic

berloquin prime puzzle

In his 1976 book 100 Numerical Games, French puzzle maven Pierre Berloquin asks whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):

1 2 3 5 7 11 13 17 19

Is it?

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No. The numbers total 78, so in a successful magic square each row and column would total a third of that, or 26. But only one of the primes is even, which means that in two rows and two columns we’d have to produce an even number by adding three odd numbers, which is impossible.

June 14, 2017June 18, 2017 | Puzzles

Black and White

matthäus chess problem

By Hans Georg Matthäus. White to mate in two moves.

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If the rook weren’t on f2 then White could immediately give mate with the knight. Unfortunately, moving the rook out of the way gives Black time to play 1. … Bd4, and now White’s plan doesn’t work — if the knight checks the king then the bishop can simply capture it. The answer is 1. Rf6! This stops the bishop from reaching d4, and Black has no way to stop 2. Nf2#.

June 6, 2017June 18, 2017 | Puzzles

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.

See full show notes …

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