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I'm no maths genius, by any means... I just thought of this, I think it's math related, and I know that SO is a good place to ask about it... So here goes:

A caterpillar can eat half it's body weight per day in leaves. It is on a bush with 12 leaves. Each leaf weighs 6 grams. Leaves grow back at a rate of 2g per leaf, per day. What's the lowest weight (whole number) it could be to eat all the leaves and how long would it take for the caterpillar to eat all the leaves?

Ross Millikan
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Hungry Little Caterpillar
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1 Answers1

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You just need the caterpillar to eat more than grows back. If so, eventually the leaves will be gone, because you aren't changing how much the caterpillar eats, nor how much grows back. So the caterpillar needs to be $48+\epsilon$ in weight. Then the leaf mass reduces by $\frac \epsilon 2$ per day and it takes $\frac {144}\epsilon$ days to eat all the leaves. There can be "end effects" if the caterpillar eats before the leaves grow. See the problem of the frog in the well.

Ross Millikan
  • 374,822
  • Did you factor in that leaves grow back at a rate of 2g per leaf, per day? (Sorry, I didn't specify that clearly) – Hungry Little Caterpillar Jan 13 '14 at 05:36
  • Yes, that is where the 48 comes from. I missed that it was 2g per leaf, that is the factor 12 from the original. The first 48g of mass eat the new leaves, then the rest eats the existing leaves. – Ross Millikan Jan 13 '14 at 05:38