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

Home > Numbers > Sequences
Deux Difference Deduction (Posted on 2015-01-23) Difficulty: 3 of 5
Find all possible arithmetic sequences of integers, with a common difference of 2, whose sum is exactly 2016.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: My revised solution | Comment 7 of 8 |
(In reply to My revised solution by Ady TZIDON)

Ady,
Both 2016 and 1007, 1009 are members of a (finite) arithmetic progression (or sequence), by definition. They also fit the definition you provided:
sequence of numbers such that the difference of any two successive members of the sequence is a constant. The definition of "any" does not discount the possibility of no members or no other members in the sequence, though it usually does imply at least one. The actual definition of a finite arithmetic sequence does not limit a sequence to three members. Even the empty set is considered valid -- though it is often excluded by some, and for the solution to this problem it would also be excluded as the empty set would definitely have no member where its sum totals 2016. I can see the argument to exclude 2016 as a solution, yet -- except by an interpretation of your definition of an arithmetic sequence -- I can not see the exclusion of 1007, 1009.

Edited on January 24, 2015, 6:51 am
  Posted by Dej Mar on 2015-01-24 04:51:45

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 (9)
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