You have nine brass rings, but three are actually gold. Can you pick these out using a balance scale three times at the most?

I am numbering the rings 1 thru 9.

I originally contemplated weighing 1 to 4 against 5 to 8; that would give me some decion on what to do with 9, but I found that I was going to run into difficulties by going down that path - run out of weighings.

I also thought about groupings of (A)123, (B)456, (C)789.  I'd put group A and B on the balance and then make some judgement as to how to break up A, B and/or C.

I recall in a Machine Programming unit about shifting/rotating digits in a certain direction.

I haven't tried this out my gut feeling is that this is the approach.

Weigh #1: I take Group A and weigh it against Group B.  And leave C on the table. 

Weigh #2: I make my observations and then rotate the rings so that 3 goes to B (on the pan), 6 goes to C (on the table), 9 goes to A (on the pan) and then I make my observations.

Weigh #3: I then repeat that process, make my observations.

I doubt that a 4th weighing would be needed as I believe by a "boolean" charting, its results would only confirm the data able to be derived from the above process.

(Other things to do - but I think that this is the foundation of the process)

Posted by brianjn on 2005-06-23 08:44:27