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

Home > Logic > Weights and Scales
Creating 5 weights (Posted on 2003-03-24) Difficulty: 2 of 5
A long time ago some ancients needed to make 5 weights that could weigh any amount of weight up to 121 grams.

The ancients though, had only a 1 gram weight and 120 grams of clay(which they would later make into weights. So with only a scale, 120 grams of clay and a 1 gram weight how would you create all the other weights needed to weigh any amount up to 121 grams?

What is the minimum amount of weighings required to do this?

See The Solution Submitted by Alan    
Rating: 3.5714 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution ? | Comment 3 of 10 |
(In reply to solution ? by Keedom)

I take it you mean that you create a 60-g weight by evenly dividing the 120 g, then a 30-g weight by evenly dividing one of the 6--g weights, etc.

However, with the now-produced set of weights being 60, 30, 15, 8 and 7, you wouldn't have anything to weigh out, say, 3 grams.

The idea is to get the 5 weights that were specified in the 5 Weights problem: 1, 3, 9, 27 and 81. These enable you from then on to weigh any integral number of grams from 1 up to 121. The 1-g weight is already present and is one of the five.
  Posted by Charlie on 2003-03-26 08:14:52

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 (8)
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