The teleporter shuts off with a hiccup and Kinesys lands on Staterion, in the middle of a square full of pendulum scales. Liz checks the panel: “The engines have to cool down for exactly fifteen minutes. Not a second more, not a second less.”
The trouble is that clocks are banned on Staterion: the Council of Scales declared them “impossible to weigh fairly.” Dord is outraged. “A planet obsessed with measurement that won’t measure time! That’s the most irrational thing I’ve ever seen.”
A kindly official hands them the only instrument allowed: two ropes and a box of matches. While she waits for an idea, Liz breaks into a few dance steps. M00N applauds.
The Riddle
You have two ropes of equal length and as many matches as you like… and nothing else! Each rope, once lit, takes exactly one hour to burn: set fire to one end, and the flame reaches the other end after exactly 60 minutes. But the ropes don’t burn evenly. They burn at random, and not even in the same way: each one does its own thing.
How can you measure exactly fifteen minutes?
Hint
A rope lit at one end measures an hour, however it burns. What happens if you light it at both ends? And nobody says you have to light the ropes one at a time.
Solution
At the start, take the first rope and set fire to both of its ends at once; at the same moment, also light one end of the second rope.
The first rope, lit from both sides, burns up completely in half an hour (it would have taken an hour if lit from one side only), no matter how irregularly it burns.
At that moment the second rope has exactly half an hour of burning left. If you now light its other end too, the two flames will meet after exactly fifteen minutes: the quarter hour you needed to measure.