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# Wipeout

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Age 11 to 16

Challenge Level

Take the numbers 1, 2, 3, 4, 5, 6 and choose one to wipe out.

For example, you might wipe out 5, leaving you with 1, 2, 3, 4, 6

The mean of what is left is 3.2

**I wonder whether I can wipe out one number from 1 to 6, and leave behind five numbers whose average is a whole number... **

How about starting with other sets of numbers from 1 to N, where N is even, **wiping out just one number**, and finding the mean?

**Which numbers can be wiped out, so that the mean of what is left is a whole number?**

**Can you explain why?**

**What happens when N is odd?**

**Here are some puzzling wipeouts you might like to try:**

One of the numbers from 1, 2, 3, 4, 5, 6 is wiped out.

The mean of what is left is 3.6

Which number was crossed out?

*With thanks to Don Steward, whose ideas formed the basis of this problem.*

The mean of what is left is 3.6

Which number was crossed out?

One of the numbers from 1 to 15 is wiped out.

The mean of what is left is $7.\dot{7}1428\dot{5}$

Which number was crossed out?

One of the numbers from 1 to N, where N is an unknown number, is wiped out.

The mean of what is left is $6.8\dot{3}$

What is N, and which number was crossed out?

One of the numbers from 1 to N is wiped out.

The mean of what is left is 25.76

What is N, and which number was crossed out?