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Erase one (Posted on 2017-05-28) Difficulty: 1 of 5
Given the numbers 1,2,3,4,…,n can you always erase one number so that the mean of the remaining numbers is an integer?

See The Solution Submitted by Ady TZIDON    
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Solution Can do Comment 1 of 1
If n is odd, erase the middle number.
If n is even, erase 1 or n.

In general, with any n numbers (not necessarily consecutive integers), calculate the sum mod (n-1), and you can succeed if one or more of those numbers have that value mod (n-1).  Clearly, with n consecutive integers, at least one will equal mod (n-1) the total mod (n-1).

  Posted by Steve Herman on 2017-05-28 10:28:07
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