Twice Blessed

When Linus Pauling won his second Nobel Prize in 1962, he joked that receiving his second Nobel was less remarkable than receiving his first: The chance of anyone receiving his first Nobel Prize is one in several billion (the population of the world), while the chance of receiving his second is one in several hundred (the number of living people who have received one prize).

What’s wrong with this argument?

Click for Answer

Side Issue

A conundrum by Russian puzzle maven Boris Kordemsky:

A work train composed of a locomotive and five cars has just stopped at a railway station when word comes that a passenger train is approaching. The smaller train must make way for it to pass through, but the station has only one siding, and this will accommodate only three cars (or an engine and two cars). How can it arrange to let the passenger train through?

Click for Answer

Flying Fur

loyd cat and dog puzzle

Sam Loyd devised this puzzle for P.T. Barnum:

A trained cat and dog run a race, one hundred feet straight away and return. The dog leaps three feet at each bound and the cat but two, but then she makes three leaps to his two. Now, under those circumstances, what are the possible outcomes of the race?

Click for Answer

Lattice Work

lattice work grid

Plot five points at random at the intersections of a coordinate grid. Between each pair of points a line segment can be drawn. Prove that the midpoint of at least one of these segments occurs at an intersection of grid lines.

Click for Answer

High Hopes

A worm crawls along an elastic band that’s 1 meter long. It starts at one end and covers 1 centimeter per minute. Unfortunately, at the end of each minute the band is instantly and uniformly stretched by an additional meter. Heroically, the worm keeps its grip and continues crawling. Will it ever reach the far end?

Click for Answer

Black and White

wheeler sui-mate

By C.H. Wheeler, from the Dubuque Chess Journal, December 1877. “White to play and compel self-mate in two moves” — that is, White must force Black to checkmate him in two moves.

Click for Answer

Heads and Tails

Let’s play a coin-flipping game. At stake is half the money in my pocket. If the coin comes up heads, you pay me that amount; if it comes up tails, I pay you.

Initially this looks like a bad deal for me. If the coin is fair, then on average we should expect equal numbers of heads and tails, and I’ll lose money steadily. Suppose I start with $100. If we flip heads and then tails, my bankroll will rise to $150 but then drop to $75. If we flip tails and then heads, then it will drop to $50 and then rise to $75. Either way, I’ve lost a quarter of my money after the first two flips.

Strangely, though, the game is fair: In the long run my winnings will exactly offset my losses. How can this be?

Click for Answer

Black and White

“The Forlorn Hope,” by J. Paul Taylor, 1878. White to mate in two moves.

Click for Answer


Cries logical Bobby to Ned, will you dare
A bet, which has most legs, a mare, or no mare.
A mare, to be sure, replied Ned, with a grin,
And fifty I’ll lay, for I’m certain to win.
Quoth Bob, you have lost, sure as you are alive,
A mare has but four legs, and no mare has five.

The Panorama of Wit, 1809