At Nails, Inc., there is a wide selection of nails. The nails are indistinguishable except for their weights.

This afternoon, you received 4 boxes full of nails. They were labeled A, B, C, and D. You were told that two of the labels were switched on accident and that you must find out which ones.

You have several scales with which you can weigh nails against each other. The people here are picky about efficiency, and you'd like to do all the weighings at once, using as few scales as possible. This means you can't change your weighing strategy according to the results of the first weighing.

What is the smallest number of scales needed to figure out which nails were switched if:

1. You know that the order from lightest to heaviest is A, B, C, then D, or

2. You know that an A nail is 1.9 g, B is 2.0 g, C is 2.1 g, D is 2.2 g.

Prove that it is the fewest number of scales needed.

(In reply to No Subject by Sing4TheDay)

I believe the problem stated  the "scales" could be used to
weigh one nail against the other.  Probably should have been
called "balances" to be precise.  
Good binary solution though.
As usual, Charlie "hit the nail on the head"
cheers

Posted by Steve Royer on 2004-07-07 23:55:40