Problem #9 MEDIUM
The Two Sand Hourglasses
Adobe Logic Lateral Thinking
Problem Statement
You need to boil an egg for exactly 9 minutes, but you do not have a clock or watch.
Instead, you have two hourglasses: one that measures exactly 4 minutes, and another that measures exactly 7 minutes.
How can you measure exactly 9 minutes using only these two hourglasses?
Answer & Quick Explanation
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Start both. Flip the 4-minute one when it empties. When the 7-minute one empties (at 7 mins), start the egg. When the 4-minute one empties again (at 8 mins), flip it to get the final 1 minute.
Detailed Editorial Solution
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We can measure exactly 9 minutes by managing the remaining sand in the hourglasses.
Here is the sequence of steps:
1. Start both the 4-minute and 7-minute hourglasses running simultaneously.
2. When the 4-minute hourglass runs out (at 4 minutes), flip it over immediately. The 7-minute hourglass now has 3 minutes of sand left.
3. When the 7-minute hourglass runs out (at 7 minutes), start boiling the egg immediately. The 4-minute hourglass (which was flipped at minute 4) now has exactly 1 minute of sand left.
4. When the 4-minute hourglass runs out (at 8 minutes), the egg has been boiling for 1 minute. Immediately flip the 4-minute hourglass over again.
5. When the 4-minute hourglass runs out this time (at 12 minutes total, 9 minutes since the egg started), stop boiling the egg.
The egg has now boiled for exactly 1 + 8 = 9 minutes (from minute 7 to minute 16). Alternatively, here is another common method:
Start both. When 4-min runs out (at 4m), flip it. When 7-min runs out (at 7m), the 4-min hourglass has 1 min left. Flip the 7-min hourglass immediately. When the 1 min in the 4-min hourglass runs out (at 8m), the 7-min hourglass has 1 min of sand at the bottom. Flip it back to run that 1 min. Total time 9 mins.