### Lights and fuses

3D Pancakes has a nice logic puzzle I’d never seen before:

Suppose you have two fuses—strings soaked in alcohol and gunpowder—and a lighter. Each fuse is carefully calibrated to take exactly one hour to burn from one end to the other. However, different portions of the fuses burn at unpredictably different rates, sometimes more slowly, sometimes faster. How would you measure exactly 45 minutes?

The answer’s at Ernie’s, along with a nice generalization of the problem: *What time intervals can we measure exactly with one-hour fuses?*

This reminds me of one of my favourite problems of this type:

In one room, there are three 100 W lightbulbs; they are all turned off. In another, there are three light switches. You don’t know which switches control which bulbs.

You are allowed to move lightswitches three times (”up” counts as moving a lightswitch once), and you are allowed to enter the room with the bulbs once. How can you tell which switches control the bulbs?

I should send these to the 13-year-old kid I mentored last year; they’ll drive her crazy, but she likes being driven crazy by things like this.

**Edited** to add that the lights all begin off and that they’re not energy efficient; thanks, Marc and Daniel Lemire.