A biochemist is cultivating living cells. Each cell splits into two cells after one minute. One minute later the two cells split to make four, then the four become eight, and so on. Every minute the number of cells doubles.

Assume that it takes an hour for one cell to grow until a bottle is filled. If the chemist starts with two cells, how long will it take to fill the same bottle?

## Solution

Some may say 30 minutes but if you think about it, the answer is 59 minutes since it only takes one minute for the cells to double in number.

I find that this puzzle is most effective when told in a casual and extempore manner. If you make it sound like just a simple puzzle, it can be rather disarming (depending on your style of delivery, of course) and some people wouldn’t give it much of a thought. I first heard this puzzle from my third-grade teacher, though I wasn’t caught off guard as I tend to listen to puzzles attentively.

I think the answer is still one hour.

If the number of cells that fills the bottle is B, then with two initial cells, in 59 minutes there will be B-1 cells. Not quite full yet. You will have to wait that extra minute to fill the bottle.

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The splitting of the cells represent a geometric sequence 1, 2, 4, 8, 16…

Beginning from 1, it requires 60 terms to fill the bottle fully. So, if we start with 2 cells (the second term of the sequence), it would only require 59 terms to completely fill the bottle.

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ah, true, the cells behave as a sequence, not a series, because the ancestors are obliterated in each succeeding generation. Not the same as saying each rabbit has two children, then those two children each have two and so on…

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Learned something. Nice blog

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Thanks.

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Reblogged this on Antonella Lallo.

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Thanks for the reblog.

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Wow! I got one right!

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A doubling time of one-minute is unrealistic, and 2^60 cells are too many to fit in a reasonable bottle—the cells would probably run out of food before the bottle was that full, switching from exponential growth phase to stationary phase. That is, cell growth is usually a logistic function rather than an exponential one—the exponential approximation is generally only good for the first 20 or 30 generations.

Maximum cell density in solution is about 10^10 cells/mL, so the bottle would have to be 115L (more of a vat than a bottle).

Perhaps mycoplasma cells could be grown to a higher volume.

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