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

Home > Just Math
What's the ... (Posted on 2013-06-27) Difficulty: 3 of 5
Start with a vector (ordered quadruplet) of any four integers. Construct a new such vector that is the difference between successive elements of the first, cyclically so that the last difference is that between the last element of the first sequence and the first element of that array. Always take the absolute value when doing the differences. Call this the "diffy" operation.

If we repeat the diffy operation starting with the sequence (3, 7, 1022, 2005) we get the following.

(3, 7, 1022, 2005)
(4, 1015, 983, 2002)
(1011, 32, 1019, 1998)
(979, 987, 979, 987)
(8, 8, 8, 8)
(0, 0, 0, 0)

True or False: Any starting sequence of integers leads to the zero vector in finitely many steps. Offer proof.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
solution?Paul2013-06-27 19:24:22
SolutionTaking the long route (spoiler)Steve Herman2013-06-27 19:23:56
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 (12)
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