PROFILE

DO THE MATH

Math and computer science professor Peter Winkler has always loved puzzles. What does he look for in selecting them for his popular books? "Amusement, universality, elegance, difficulty and," says Winkler, "solvability." Here is a puzzler drawn from his Mathematical Puzzles: A Connoisseur's Collection. A second collection, Mathematical Puzzles That Boggle the Mind, is due out in August.

THE ATTIC LAMP SWITCH: A downstairs panel contains three on-off switches, one of which controls the lamp in the attic—but which one? Your mission is to do something with the switches, then determine after one trip to the attic which switch is connected to the attic lamp.

Solution: It really is impossible to tell which switch is connected to the attic lamp if all you get is one bit of information from your trip to the attic. However, you can get more information with your hand! Turn on Switches I and 2, wait a few minutes, then turn off Switch 2 before ascending to the attic. If the bulb is off but warm, you conclude that Switch 2 is the winner. If you can't reach the bulb but have enormous patience, you can achieve the same effect by turning Switch 2 on and then waiting a couple of months before turning on Switch I and visiting the attic. If the bulb is burnt out, Switch 2 is the culprit.