A frog is at the bottom of a 10-foot well. Each day he climbs 3 feet and slips back 2 feet at night. After how many days does he escape the well?
The frog in the well
#1
The frog in the well
Posts
Re: The frog in the well
#298
Re: The frog in the well
#3
Ten days
Re: The frog in the well
#47, unless he slips as he steps out and slides back 2 feet, then 8. Had a gray tree frog once living in my downspout barrel. He came out at night and crawled onto a kitchen window. His singing reverberated throughout the house. It was neat at first, then annoying.
Re: The frog in the well
Edited Solution #5
I don't have an official answer to this, but mine matches Dale's. Here's my reasoning assuming he escapes as soon as he climbs to or above 10 feet during the day, before slipping back.
Day 1: Starts at 0 feet, climbs to 3 feet, slips back to 1 foot.
Day 2: Starts at 1 foot, climbs to 4 feet, slips back to 2 feet.
Day 3: Starts at 2 feet, climbs to 5 feet, slips back to 3 feet.
Day 4: Starts at 3 feet, climbs to 6 feet, slips back to 4 feet.
Day 5: Starts at 4 feet, climbs to 7 feet, slips back to 5 feet.
Day 6: Starts at 5 feet, climbs to 8 feet, slips back to 6 feet.
Day 7: Starts at 6 feet, climbs to 9 feet, slips back to 7 feet.
Day 8: Starts at 7 feet, climbs to 10 feet (3 + 7 = 10). Since he reaches 10 feet during the day's climb, he escapes before slipping back.
Added later 04 min:
Note that the forum has a feature to flag a reply as a "solution" which appears as a check mark both next to the reply and the topic on the index page. Here I am using it to mark the correct answer.