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8 days.

I say 10 days. Day 1, jumps 3 feet, slides back 2 feet equals 1 foot up on Day 1. Day 2, jumps 3 feet, slides back 2 feet equals 1 foot up on Day 2, plus 1 from Day 1 = 2 feet.

Day 3, jumps 3 feet, slides back 2 feet equals 1 foot up on Day 3, plus 1 from Day 1 and 1 from Day 2 = 3 feet.

etc. until Day 10 when his jumps total ten feet up.

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Q: How long will it take a monkey to reach the top if the monkey is at the bottom of a well ten feet deep and each day he jumps up 3 feet and slips back two?
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