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 sum of the first n natural numbers is n(n+1)/2. Subtracting a deleted number,d, gives n(n+1)/2-d, making the average (n(n+1)-d)/(2(n-1)).

With the 271/16 average, this makes
d=(n(n+1)-542(n-1))/2

This is negative for n<32.

When n=32 the result for d has a fraction; n = 33 gives d=19; for n>33, d would be larger than n, and thus is impossible.

So N is 33 and 19 was the deleted number.

Posted by Charlie on 2003-08-27 16:16:27