Problem #2 EASY
Burning Ropes of Time
Microsoft Math Lateral Thinking
Problem Statement
You are given two ropes of uneven density and a box of matches. Each rope takes exactly 60 minutes (1 hour) to burn completely from one end to the other.
Because the ropes have uneven density, they do not burn at a constant rate. For example, half of a rope might burn in 10 minutes while the remaining half takes 50 minutes. You cannot cut the ropes or measure them by length.
How can you use these ropes to measure exactly 45 minutes?
Answer & Quick Explanation
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Light the first rope at both ends and the second rope at one end. When the first rope finishes burning (30 mins), light the other end of the second rope to measure another 15 minutes.
Detailed Editorial Solution
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Since each rope burns for exactly 60 minutes, lighting a rope from both ends simultaneously will cause it to burn completely in exactly half the time, which is 30 minutes, regardless of its density distribution.
To measure exactly 45 minutes:
1. Start by lighting Rope A at both ends, and Rope B at only one end.
2. Rope A will burn out completely in exactly 30 minutes. At this exact moment, Rope B has been burning for 30 minutes, meaning it has exactly 30 minutes of burn time remaining.
3. The moment Rope A goes out, light the other end of Rope B. Because Rope B is now burning from both ends, its remaining 30 minutes of burn time will be cut in half, taking exactly 15 minutes to burn out completely.
The total time elapsed from the beginning until Rope B completely burns out is 30 minutes + 15 minutes = 45 minutes.