The snail and the wall
A snail starts at the foot of a wall 30 feet high. Every hour it climbs 3 feet and then slips back 2 feet.
After how many hours does it first reach the top?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
The net progress is 1 foot per hour, but what happens during the last hour?
Once the snail reaches the top during a climb, it does not slip back.
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s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. The snail gains 1 foot per hour, except in the last hour, when the 3-foot climb takes it over the top before any slip.
Step 1. After full hours (climb and slip), the snail is at feet.
Step 2. It reaches the top during the climb of hour if , that is .
Step 3. After 27 hours it is at 27 feet, and the climb of the 28th hour takes it to 30 feet. So the answer is 28 hours.
The trap. “1 foot per hour, so 30 hours” ignores that the last climb does not need the slip.