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What is the smallest weight that can be weighed using the following coins?
I have a number of coins with weights (in grams) as follows:
One pence 3.56g
Two pence 7.12g
Five pence 3.25g
Ten pence 6.50g
Twenty pence 5.00g
Fifty pence 8.00g
One pound 9.50g
Two pound 12.00g
What is the smallest weight I can weigh (in hundredths of a gram) using any number of coins and a balance? What combination of coins do I need to use and what is the smallest value needed?
It is assumed that the balance is sensitive enough to register at least the minimum weight required.
We can do better than 0.19 grams, I think!
2 Answers
- 9 years agoFavourite answer
The smallest weight I can see that can be weighed is 0.04 grams.
Place 9 one pence pieces on one side of the balance = 32.04g
Place 4 fifty pence pieces on the other side of the balance = 32.00g
The difference is 0.04g, so any multiple of 0.04 grams ought to be possible but the sequence also includes differences which are not multiples of 0.04, so smaller differences may be possible.
- 9 years ago
Put 1p, 5p, and 20p (=11.81g) on side A. Put £2 (12.0g) on side B. can then weigh object of only 0.19g on side A.
