Easy | General |

You are given two cords that both burn exactly one hour, not necessarily with constant speed. How should you light the cords in order to determine a time interval of exactly 15 minutes? Extra question: how to light just one cord and measure 15 minutes?

Hint

Because this lacks uniformity, we cannot break the cord in half, and expect it to burn in half the time. But we can burn both ends of a cord to finish it in half the time it would have taken otherwise!

Solution

Burn first cord at one end and the second cord at both ends. Half an hour later, second cord finishes burning. Now you can burn the other end of first cord, and it shall finish exactly in 15 minutes.

Now can you guess how to measure 15 minutes using only one cord?

Break the cord into approximately half, and burn these two cords form both their ends. If both these cords finish burning together, that means exactly 15 minutes have passed. If any one of these cords finishes first, break the other cords from approximately middle, and further burn all ends of these little cords. Continuing this way theoretically leads to exactly 15 minutes!

Now can you guess how to measure 15 minutes using only one cord?

Break the cord into approximately half, and burn these two cords form both their ends. If both these cords finish burning together, that means exactly 15 minutes have passed. If any one of these cords finishes first, break the other cords from approximately middle, and further burn all ends of these little cords. Continuing this way theoretically leads to exactly 15 minutes!

Source: Quant Interview

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