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

Home > Just Math
Restoring the erased (Posted on 2010-07-14) Difficulty: 3 of 5
The following text represents a valid contest question
in which I have erased one number :

Let S be a set of 20 distinct positive integers,
each less than EN(=THE ERASED NUMBER).
Show that there exist four distinct elements a, b, c, d , all in S,
such that a + b = c + d.

What maximal value of EN guarantees the existence of these elements ?

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): High-Low-Jack... | Comment 3 of 21 |
(In reply to re: High-Low-Jack... by Dej Mar)

I think F(21) is a good surmise (so an excluded set of 20 would be F(2)=1 thru F(21)=10946). F(0)=0 is not positive, and F(1) and F(2) are both = 1 (can't repeat same number).  I was suggesting 17711 which is F(22)+1 to "play it safe" but no proof.

The wording of the puzzle still gives me pause.  We would both be setting an upper bound for EN such that not all sets of twenty with that EN limit have the requisite sums (by "construction" using the Fibonacci series).  But what would rule out a lower EN which still had the property that some set S might not in fact allow the equation for some subset of four members?  A set S could easily be verified, if found , but the exponential search space would seem to be prohibitive.


  Posted by ed bottemiller on 2010-07-14 20:20:58
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information