MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

June 1, 2007

Solve It or Die

It's a tense moment in Die Hard with a Vengeance. A time bomb is about to go off. The frazzled heroes, detective John McClane and his sidekick Zeus, a dry cleaner from Harlem, have just seconds to defuse it. To their horror, they discover they must solve a mathematical puzzle to do so.

Sitting on the lip of a fountain in a park are a 5-gallon jug and a 3-gallon jug. The timer will stop if they place a jug containing 4 gallons of water on a scale attached to the bomb.

Bumbling about, our heroes realize that it won't do to use the smaller jug to pour 3 gallons into the larger one, then refill the smaller jug one-third of the way up to get the extra gallon. The villain, being a villain, had insisted that the total amount be exactly 4 gallons.

The puzzle that John and Zeus have to solve has actually been around for a long time—at least since the 1200s, to be exact. You often find it in collections of brainteasers. Can you solve it—in less than 30 seconds? One solution is given below. Can you think of another?

After a lot of yelling and confusion, John and Zeus solve the puzzle, stop the timer, and save the day. But if you watched this particular scene closely (doubtful, since the movie is rated R), you'd have seen that it wasn't filmed very carefully. Water levels in the jugs rise and fall throughout the sequence without human intervention. Some Hollywood magic, perhaps?

There are lots of puzzles that involve measuring out given amounts using various jugs. Here's another one for you to try: Given an 11-gallon jug and a 4-gallon jug, measure out exactly 1 gallon. Maybe this puzzle, or another one like it, will show up in the fourth Die Hard movie.

How to Measure Out 4 Gallons
• Fill the 5-gallon jug.
• Empty the 5-gallon jug into the 3-gallon jug, leaving 2 gallons.
• Empty the 3-gallon jug.
• Pour the 2 gallons from the 5-gallon jug into the 3-gallon jug.
• Fill the 5-gallon jug and use it to fill the 3-gallon jug. That leaves 4 gallons in the 5-gallon jug.

Muse, March 2004, p. 45.