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 ?

You can't affect the average by more than 0.5 by removing any number so the given average (271/16 =16.9375) gives a good estimate of the original N simply by doubling (33.875)
The original N is therefore around 32-34
Then the denominator gives away the new list has 32 numbers totalling 542 (271/16 doesn't break so N-1 must be a multiple of 16) making the original N 33 with a total of 561 ((33sq+33)/2).
The 19 difference is the missing number.

Posted by Lee on 2003-08-28 02:27:12