# Three by Three

What’s the ratio between the areas of the two triangles?

# Well Traveled

In Lord Dunsany’s Fourth Book of Jorkens, a member of the Billiards Club observes a book called On the Other Side of the Sun and says, “On the other side of the sun. I wonder what’s there.”

Jorkens, to everyone’s surprise, says, “I have been there.”

Terbut challenges this, but Jorkens insists he was on the other side of the sun six months ago. Terbut knows perfectly well that Jorkens was at the club six months ago, so he wagers £5 that Jorkens is wrong. Jorkens accepts.

“You have witnesses, I suppose,” says Terbut.

“Oh, yes,” says Jorkens.

“My first witness will be the hall-porter,” says Terbut. “And yours?”

“I am only calling one witness,” says Jorkens.

“Went with you to the other side of the sun?” asks Terbut.

“Oh, yes,” says Jorkens. “Six months ago.”

“And who is he?” asks Terbut.

Whom did Jorkens call?

# Black and White

By William Anthony Shinkman. White to mate in two moves.

# Alcohol Problem

A bottle of fine wine normally improves with age for a while, but then goes bad. Consider, however, a bottle of EverBetter Wine, which continues to get better forever. When should we drink it?

— John L. Pollock, “How Do You Maximize Expectation Value?”, Noûs, September 1983

See The Devil’s Game.

# Out of Sight

Several spherical planets of equal size are floating in space. The surface of each planet includes a region that is invisible from the other planets. Prove that the sum of these regions is equal to the surface area of one planet.

You and I drive from Los Angeles to Las Vegas in separate cars. We depart simultaneously, and you stay always ahead of me, dutifully driving the speed limit throughout the trip. Nonetheless I get ticketed for speeding. How?

# Black and White

From Deutsche Schachzeitung, 1890. White to mate in two moves.

# Animal Behavior

Martian snakes are elastic. If you take the tail of a Martian snake, and I take the head, and we pull in opposite directions, will there always be a part of the snake that doesn’t move?

# Reverses

A Hungarian problem shortlisted for the 30th International Mathematical Olympiad, 1989:

Around a circular race track are n race cars, each at a different location. At a signal, each car chooses a direction and begins to drive at a constant speed that will take it around the course in 1 hour. When two cars meet, both reverse direction without loss of speed. Show that at some future moment all the cars will be at their original positions.

# Black and White

By B.J.M. Markx, 1897. White to mate in two moves.