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After years of experiments, you've finally created the pets of the future,

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nanorabbits.

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They're tiny, they're fuzzy, and they multiply faster than the eye can see.

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In your lab, there are 36 habitat cells,

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arranged in an inverted pyramid, with eight cells in the top row.

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The first has one rabbit, the second has two, and so on,

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with eight rabbits in the last one.

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The other rows of cells are empty, for now.

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The rabbits are hermaphroditic,

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and each rabbit in a given cell will breed once

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with every rabbit in the horizontally adjacent cells,

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producing exactly one offspring each time.

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The newborn rabbits will drop into the cell

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directly below the two cells of its parents

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and within minutes will mature and reproduce in turn.

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Each cell can hold 10 to the 80th power nanorabbits.

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That's a 1 followed by 80 zeros before they break free and overrun the world.

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Your calculations have given you a 46-digit number

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for the count of rabbits in the bottom cell.

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Plenty of room to spare.

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But just as you pull the lever to start the experiment,

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your assistant runs in with terrible news.

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A rival lab has sabotaged your code

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so that all the zeros at the end of your results got cut off.

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That means you don't actually know

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if the bottom cell will be able to hold all the rabbits,

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and the reproduction is already underway.

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To make matters worse,

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your devices and calculators are all malfunctioning,

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so you only have a few minutes to work it out by hand.

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How many trailing zeros should there be

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at the end of the count of rabbits in the bottom habitat?

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and do you need to pull the emergency shutdown lever?