# Waste Not …

A puzzle from Polish mathematician Paul Vaderlind:

John is swimming upstream in a river when he loses his goggles. He lets them go and continues upstream for 10 minutes, then decides to turn around and retrieve them. He catches up with them at a point one half mile from the point where he lost them. Is the river flowing faster than 1 mile per hour? (Assume that John swims at the same strength throughout.)

# 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?

# 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?

# Flying Fur

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?

# Lattice Work

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.

# Black and White

By William Crane Jr., from the Sydney Town and Country Journal, 1877. White to mate in two moves.

# 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?

# Black and White

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.