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 Multipan Balance (Posted on 2009-01-18)
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: ( Back to comment list | You must be logged in to post comments.)
 Some thoughts | Comment 2 of 3 |
Proof by mathematical induction is the way to go!

 Posted by elementofsurprize on 2009-01-20 20:31:53

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