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

Home > Numbers
Erase the right 90 (Posted on 2016-01-28) Difficulty: 3 of 5
101 distinct real numbers are written in any order

Prove that it is possible to erase 90 of them leaving a sequence of 11 numbers that are in either a strictly increasing or strictly decreasing order.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re: proof on the internet (spoiler) | Comment 3 of 5 |
(In reply to proof on the internet (spoiler) by Charlie)

Actually, I find the puzzle itself difficult to follow.

On my bookshelf I have the ten-volume set of K.Sengupta's collected problems. As is well known, by some whimsy of the author, each volume has a real number 1.x, 2.x, 3.x, etc. We shall call these 1,2,3.. for short.

Assume I order them: 1,10,2,9,3,8,4,7,5,6. I see no continuous subsequence of four here which is either strictly increasing or decreasing.

But if the subsequence can be non-continuous, e.g. we can rub out 10, and select 1,2,3,4 as our four-part sequence, then a more challenging problem (by far) is to arrange volumes 1 to 9 in some order such that there is no non-continuous sequence of four that is either strictly increasing or strictly decreasing, given that either is acceptable.

Edited on January 29, 2016, 7:47 am
  Posted by broll on 2016-01-29 07:37:57

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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information