All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
The Deleted Number (Posted on 2003-08-27) Difficulty: 3 of 5
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 ?

  Submitted by Ravi Raja    
Rating: 2.6667 (3 votes)
Solution: (Hide)
19 was removed from the first 33 counting numbers.

N-1 must be a multiple of 16, since we are dealing with natural numbers and the average of N-1 numbers is a rational number which reduces to have 16 as the denominator.

Also, the average for the first n natural numbers is just n/2. 16²=256, so 271/16 is just a little more than 16. By inspection, we can guess that there were 33 numbers, with an average of a little more than 16, and after 1 is erased, the average of the remaining n-1 numbers is also relatively close to 16.

For 32 numbers to have an average of 271/16, their sum must be 271×2=542. The total of the first 33 numbers is 561, a difference of 19, so 19 must have been the number that was removed.

Charlie posted a solution based on the algebraic formulas involved, here.
Also, DJ posted a general method for solving this problem given any value for the average; that can be found here.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle Solution: Method IIIK Sengupta2022-02-06 23:09:29
Puzzle SolutionK Sengupta2022-02-06 22:22:11
SolutionPuzzle Solution: Method IIK Sengupta2022-01-27 02:01:27
SolutionPuzzle Solution: Method IK Sengupta2022-01-27 01:40:53
AnswerK Sengupta2022-01-27 01:25:04
The solutionRichard Briscoe2003-09-03 04:09:33
SolutionSolutionLawrence2003-08-28 02:38:18
another 'method'?Lee2003-08-28 02:27:12
SolutionSolution MethodDJ2003-08-27 16:39:21
Solutionanother methodCharlie2003-08-27 16:16:27
re: spoilerYour buddy2003-08-27 15:24:46
My solutionH2003-08-27 15:22:02
SolutionspoilerYour buddy2003-08-27 15:13:41
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information