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

Home > Logic > Weights and Scales
Weights that check themselves. (Posted on 2010-11-23) Difficulty: 3 of 5

Assume an old-fashioned scale balance in which weights can be placed on either side. The associated set of weights (each of which is greater than zero) is 'complete' for some W if it is capable of measuring all integer weights from 1 to W.

Clearly it is possible for such sets to exist even if no combination of the weights themselves can be balanced against any combination of the remaining weights - the set {1,2,4,8..} is just one such example.

On the other hand, the set {1,1,2,4} is also 'self-measuring', because, assuming that one of the weights were unmarked, a stranger could neverthless establish its value by weighing it in the scales with the others.

Question: You are allowed 5 weights. They must form a set which is complete, and also self-measuring.

What is the largest possible value of W, given these constraints?

Bonus: What is the largest possible value of W, if 8 weights are allowed?

See The Solution Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 4 of 6 |
(In reply to solution by Justin)

unfortunately, I believe that your submissions fail to meat the self-measuring requirement.  For example, with {1,3,9,27,81} you are not able to weight the "1" weight using only the remaining weights, namely {3,9,27,81}, no possible selection of these remaining weights will allow you to weight 1.  However, your insight does provide us with a theoretical maximum, although it remains to be seen if it is possible to achieve it.

please see my next post for the initial results of my computer search.


  Posted by Daniel on 2010-11-24 05:26:41
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 (6)
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