By J. Berger. White to mate in two moves.

# Puzzles

# The Candy Thief

A problem by Wayne M. Delia and Bernadette D. Barnes:

Five children — Ivan, Sylvia, Ernie, Dennis, and Linda — entered a candy store, and one of them stole a box of candy from the shelf. Afterward each child made three statements:

Ivan:

1. I didn’t take the box of candy.

2. I have never stolen anything.

3. Dennis did it.

Sylvia:

4. I didn’t take the box of candy.

5. I’m rich and I can buy my own candy.

6. Linda knows who the crook is.

Ernie:

7. I didn’t take the box of candy.

8. I didn’t know Linda until this year.

9. Dennis did it.

Dennis:

10. I didn’t take the box of candy.

11. Linda did it.

12. Ivan is lying when he says I stole the candy.

Linda:

13. I didn’t take the box of candy.

14. Sylvia is guilty.

15. Ernie can vouch for me, because he has known me since I was a baby eight years ago.

If each child made two true and one false statement, who stole the candy?

# The Windmill Algorithm

Suppose we have a finite set of points in the plane, no three of which are collinear. A line drawn through one of them pivots around that point until it encounters another point, when it adopts that point as the new pivot. Call this line a “windmill”; it continues indefinitely, always rotating in the same direction. Show that we can choose an initial point and line so that the resulting windmill uses each point as a pivot infinitely many times.

# Black and White

By Berthold Weiß. White to mate in two moves.

# The Mengenlehreuhr

Further to Saturday’s triangular clock post, reader Folkard Wohlgemuth points out that a “set theory clock” has been operating publicly in Berlin for more than 40 years. Since 1995 it has stood in Budapester Straße in front of Europa-Center.

The circular light at the top blinks on or off once per second. Each cell in the top row represents five hours; each in the second row represents one hour; each in the third row represents five minutes (for ease of reading, the cells denoting 15, 30, and 45 minutes past the hour are red); and each cell in the bottom row represents one minute. So the photo above was taken at (5 × 2) + (0 × 1) hours and (6 × 5) + (1 × 1) minutes past midnight, or 10:31 a.m.

Online simulators display the current time in the clock’s format in Flash and Javascript.

If that’s not interesting enough, apparently the clock is a key to the solution of Kryptos, the enigmatic sculpture that stands on the grounds of the CIA in Langley, Va. In 2010 and 2014 sculptor Jim Sanborn revealed to the *New York Times* that two adjacent words in the unsolved fourth section of the cipher there read BERLIN CLOCK.

When asked whether this was a reference to the Mengenlehreuhr, he said, “You’d better delve into that particular clock.”

# Black and White

By Pierre Auguste D’Orville. White to mate in two moves.

# The Perplexed Cellarman

One last puzzle from Henry Dudeney’s *Canterbury Puzzles*:

Abbott Francis sends for his cellarman and complains that a particular bottling of wine is not to his taste. He asks how many bottles he had produced. The cellarman tells him that there had been 12 large and 12 small bottles, and that 5 of each have been drunk. The abbot replies that three men are waiting at the gate, and orders the cellarman to give each of them some combination of full and empty bottles so that each man receives the same quantity of wine and combination of bottles.

How can the cellarman do this? He has seven large and seven small bottles full of wine, and five large and five small bottles that are empty. A large bottle holds twice as much wine as a small one, but a large bottle when empty is not worth two small ones — hence the abbot’s order that each man must take away the same number of bottles of each size.

# Crying Wolf

A puzzle from reader Paul Sophocleous:

Van Helsing, who is of course famous for his part in the destruction of Dracula, has had many other encounters with supernatural creatures. In the early hours of one morning, he was woken by a loud knock at the door. “Come quickly!” cried the chief of police. “There’s been a ghastly attack at the manor house on the hill!”

Van Helsing dressed hurriedly and followed the chief. A grisly sight met him when he arrived. The front door of the house was open, and the beam of light that came from within shone on the body of a young man lying on the path. His throat had been torn out viciously, as though he had been attacked by some kind of hideous wild beast. Van Helsing looked around, but the grounds were dark, since the moon had set some time before, and he could see nothing else.

He stepped inside and found that several officers of the local constabulary were comforting a woman who appeared to be the maid. “It was horrible!” she cried. “I came down here after hearing some racket outside, and I found the young master at the door. ‘There’s something out there,’ he told me, ‘some beast, and I mean to drive it off.’ And he had in his hand the poker from the fireplace as a weapon. But when he opened the door, it was on him in a flash, a great beast, all hairy and shaggy, bigger than a man it was!”

Van Helsing stepped forward. “What was it?” he demanded.

The maid let out a little scream and gasped, “It was a werewolf!” And with that she fainted dead away.

“Could it be, Van Helsing?” said the chief, sounding worried.

Van Helsing shook his head. “Not a chance.”

Why not?

# A Compensatory Harmonica

A problem from the *American Mathematical Monthly*, March 1930:

Two men jointly own *x* cows. They sell these for *x* dollars per head and use the proceeds to buy some sheep at $12 per head. Their income from the cows isn’t divisible by 12, so they buy a lamb with the remainder. Later they divide the flock so that each man has the same number of animals. This leaves the man with the lamb somewhat short-changed, so the other man gives him a harmonica. What’s the harmonica worth?

# Podcast Episode 135: Lateral Thinking Puzzles

Here are six 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.