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A leak in the roof allows two drops through the first day, four drops through the second day, eight drops the third.
At this rate, when will the 500th drop fall through? Show your work.
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Anybody can solve this easy problem by making a Table similar to that below.
day drops total total
this day drops drops+2
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1 2 2 4
2 4 6 8
3 8 14 16
4 16 30 32
5 32 62 64
6 64 126 128
7 128 254 256
8 256 510 512
From the table, one can see that the 500th drop will fall on the 8th day.
If you want to create a theory around it, then add and consider
an additional column (the last column in the table) by adding 2
to the numbers in the 3rd column. All these numbers are
of the form , where "n" is a sequential number of the day.
Then you can conclude that 500th drop will fall when n+1 = 9 ( = 512 ), or n = 8.
Solved.