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 ?
(In reply to
spoiler by SilverKnight)
If you'd like an easy way to solve this...
recognize that the 271/16 can't be reduced any further, therefore the total (to create that average) must be 16 numbers totalling 271, or 32 numbers totalling 542, or 48 numbers totalling 813, etc.
Since the professor wrote Natural numbers and the student took one away, we're talking about 1-17 less one of the digits, or 1-33 less one of the digits, or 1-49 less one of the digits, etc.
If we total the first 17 numbers, we find the total is 153. TOO LOW! We can't subtract one number and find the requisite 271.
If we total the first 49 numbers, we find the total is 1225. TOO HIGH! We can't subtract one number and find the requisite 813.
But (we probably would've tried this by now), if we total the first 33 numbers, we find the total is 561... hmmm.... we need a total of 542.... so subtract 19! And there we go.
Edited on August 27, 2003, 3:27 pm
re: spoiler
