Whats the answer with these frogs in the well?!


Question: A frog falls to the bottom of a 20 meter well. In the struggle to get out, during the day the frog climbs 3 meters up the wall. During the night the frog slips back 2 meters.
How many days will it take to escape?


Answers: A frog falls to the bottom of a 20 meter well. In the struggle to get out, during the day the frog climbs 3 meters up the wall. During the night the frog slips back 2 meters.
How many days will it take to escape?

18 days he's not gonna' fall back 2 after he gets out.

20 days

so the poor frog averages a total of one meter gained per day (essentially) right?
so 20 days I guess

18

17? no its 19 days? Oh, 18...

About 20 days

17 days

Day 1: start at 0 (from bottom), climb up 3 to +3, slip back 2 to +1.
Day 2: start at +1, climb to +4, slip back to +2.
Day 3: start at +2, climb to +5, slip back to +3.
Day 4: start at +3, climb to +6, slip back to +4.
Day 5: start at +4 (where yesterday ended), climb (+3) to +7, slip back (-2) to +5.
...
(Got the pattern, now? OK, let's skip to 10 days later!)
...
Day 15: start at +14, climb to +17, slip back to +15.
(Just add one to each number, for the next day.)
Day 16: start at +15, climb to +18, slip back to +16.
Day 17: start at +16, climb to +19, slip back to +17.
Day 18: start at +17, climb to +20 ....

Hey, that's it!
Silly frog hops away on day 18, and doesn't hang around.

18 days is the answer.
.



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