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?

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?

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?

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?

By J.R.G. De Veer. White to mate in two moves.

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*.

A puzzle by Frank Morgan: The meaning of a common English word becomes plural when an A is added at its start. What is the word?

A puzzle by MIT mathematician Tanya Khovanova:

Three logicians walk into a bar. Each is wearing a hat that’s either red or blue. Each logician knows that the hats were drawn from a set of three red and two blue hats; she doesn’t know the color of her own hat but can see those of her companions.

The waiter asks, “Do you know the color of your own hat?”

The first logician answers, “I do not know.”

The second logician answers, “I do not know.”

The third logician answers, “Yes.”

What is the color of the third logician’s hat?

Richard Hess posed this problem in the Spring 1980 issue of *Pi Mu Epsilon Journal*. At noon on Monday, a bug departs the upper left corner, X, of a p × q rectangle and crawls within the rectangle to the diagonally opposite corner, Y, arriving there at 6 p.m. He sleeps there until noon on Tuesday, when he sets out again for X, crawling along another path within the rectangle and reaching X at 6 p.m. Prove that at some time on Tuesday the bug was no farther than p from his location at the same time on Monday.

During a visit to Crete in 1938, Miss L.S. Sutherland described a game she saw played on a pentagram:

You have nine pebbles, and the aim is to get each on one of the ten spots. You put your pebble on any unoccupied spot, saying ‘one’, and then move it through another, ‘two’, whether this spot is occupied or not, to a third, ‘three’, which must be unoccupied when you reach it; these three spots must be in a straight line. If you know the trick, you can do this one-two-three trick, for each of your nine pebbles and find it a berth, and then you win your money. If you don’t know the trick, it’s extremely hard to do it.

To make this a bit clearer: The figure has 10 “spots,” the five points of the star and the five corners of the pentagon in the middle. A move consists of putting a pebble on any unoccupied spot, moving it through an adjacent spot (which may be occupied) and continuing in a straight line to the next adjacent spot, which must be unoccupied. You then leave the pebble there and start again with a new pebble, choosing any unoccupied spot to begin this next move. If you can fill 9 of the 10 spots in this way then you’ve won.

Can you find a solution?

By T.R. Dawson. “The problem is for each White man to capture the corresponding Black man in such a way that the routes traversed by each man never come in contact with one another.”