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# Set nibbling

### #1

Posted 02 May 2014 - 10:45 AM

From the set of integers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} I randomly choose an element, say 3. I subtact 3 from 10, getting 7.

Now I have the set {1, 2, 3, 4, 5, 6, 7}. I choose another element at random, say 5. I subtract 5 from 7, getting 2.

Now I have the set {1, 2}. I randomly choose one of these elements, say 1. I subtract 1 from 2, getting 1.

Now I have the set {1}. I randomly choose one of these elements. It turns out to be 1. I subtract 1 from 1, getting 0.

Now I have the empty set.

Each step took away a nibble, leaving a smaller set.

This example nibbled a set of 10 elements down to zero in four steps.

Starting with a set of * p* elements, what is the expected number

*of nibbles required to empty the set?*

**n**

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 02 May 2014 - 11:50 PM Best Answer

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