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A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.

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Posted · Report post

30 days

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On day 1, he jumps up to 27 meters below the surface, but then slips down to 29 meters down.

On day x, he jumps up to 28-x meters below the surface, but slips to 30-x during the night.

Since we want the day for which he jumps to 0 meters below, we solve 28-x = 0 for x.

Obviously it is on day 28 that the frog is free from his cylindrical prison.

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30 days

A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one

The frog leaps up the well 3m during the day, but slips 2 meters backwards during the night ==> effectively, he moved up 1 m per day (24hrs).

To climb up 30m, he will need then 30 days.

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-Supposing the well is the type that goes above the surface.

-Supposing that when he lands at the lip of the well he will not anymore fall

Out when already on the lip:

With him going up 3 meters and falling two it is as though you are saying he goes up 1 meter per day. He gets to 3 meters away from the top in 27 days, and with a three meter jump will get on the lip of the well.

=28 days

Has to get of the lip:

Same as above solution though adding an extra day to get off the lip of the well.

=29 days

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After the 27th day the frog is 3 meters from the top.

The next day he jumps out.

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After the 27th day the frog is 3 meters from the top.

The next day he jumps out.

Ahhh ... I got it now.

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Posted · Report post

29 days. It is basicly how puzzled and bonanova explained it

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29 days. It is basicly how puzzled and bonanova explained it

so you're saying (like puzzled said) that the frog needs to get above the lip to get out? if this is the case, then wouldn't the frog's hind legs be exactly 30 m from the bottom of the well, which is exactly 0 m from the top of the well? he should be able to get out then because his whole body is above the lip of the well because his hind legs are exactly 0 m from the top of the well. am i correct or did i miss something? :huh:

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Posted · Report post

my bad bonanova did NOT have the correct answer

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If ESCAPE FROM WELL means getting to the top of well, then 28 days...if it means getting AWAY from well then 29 days

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Posted · Report post

28 Because the hind legs go up 3m.

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