The snail climbing out of the well

Question

A snail is at the bottom of a well 10 meters deep. Each day it climbs 3 meters up, but each night while resting it slips 2 meters back down. How many days does it take the snail to climb out of the well? (The obvious answer is wrong.)

Accepted Answer

The snail escapes on day 8, not day 10. The trap. Net progress per full day-night cycle is 3 - 2 = 1 meter, so it's tempting to say the snail needs 10 days to climb 10 meters. But that ignores the crucial detail: once the snail reaches the top during the day, it's out, it never slips back that night. Track it carefully. Measure height at the end of each night (after the slip): - End of night 1: 3 - 2 = 1 m - End of night 2: 1 + 3 - 2 = 2 m - End of night 3: 3 m - ... - End of night k: k meters. So after each night the snail sits at exactly k meters. On the next day it climbs 3 more. It escape…

The snail climbing out of the well

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