A professor writes N consecutive natural numbers, beginning with 1, on the blackboard. One of the students in the class deletes one of the numbers (exactly one number), from that list.
Now, given that the average of the remaining N-1 numbers is 271/16.
Can you find out the number that has been deleted from the list ?

The 16 in the denominator hints that (N-1) is divisible by 16. Then the numerator would have to be 271x, where x = (N-1)/16. Thus, we must find a number n = 16x+1 whose summation is at most n greater than 271x

If N-1 were to equal 16, then N itself would be 17. However, then Sum(N-1) would be at most 152 (if 1 was deleted), which obviously cannot be the case.

Trying N-1 = 32, we find a solution. At N = 33, Sum(N) = 561, and 271x=542. 561-542=19.

Thus, it was the number 19 that was deleted

Posted by H on 2003-08-27 15:22:02