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

Home > Logic > Weights and Scales
Multipan Balance (Posted on 2009-01-18) Difficulty: 3 of 5
A multipan balance scale depicted below has one pan on the left and five on the right.
-+-       -+-  -+-  -+-  -+-  -+-
 |         |    |    |    |    |
 +----+----+----+----+----+----+
      |
      |
The pan on the left is a unit distance from the fulcrum. The pans on the right are 1, 2, 3, 4, and 5 units from the fulcrum. The balance scale is operated by placing an unknown weight on the left and placing some or all of a known set of weights on the pans on the right.

If the known weights are 1, 2, 3, 4 and 5, show that any integral weight 1 to 75 can be measured. What is the smallest measurement requiring 3 weights on the right? 4 weights? 5 weights?

If the restriction that only one weight can occupy a pan is added, show that any integral weight 1 to 55 can be measured. What is the smallest measurement requiring 3 weights on the right? 4 weights? 5 weights?

No Solution Yet Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Proof of first part by mathematical inductionelementofsurprize2009-01-22 19:48:39
Some ThoughtsSome thoughtselementofsurprize2009-01-20 20:31:53
Solutioncomputer solutionCharlie2009-01-18 16:54:22
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 (1)
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