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 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?