This represents a circular balance.

                       
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A light circular disk is needle point mounted. It has a graduated scaled track "o" from which identical measuring pans may be suspended.

Suggest the minimum number of pans as well as the minimum weighings needed, and the strategy required to determine which one of 9 coins is in weight variance with the other 8 in a visually identical collection. You should also be able to determine if the variant coin is lighter or heavier than each of the others.

At the end of each weighing, the coins being weighed will be on the balance, and the balance will be in equilibrium.

For additional discussion:
The set of nine has 7 regular coins with one weighing lighter, and the other weighing heavier than the others.
How might the circular balance assist?
Does a disparate difference in weight of the lighter to the normal than the heavier to normal influence the procedure? [This thought was raised at review.]

(In reply to re: part 1 solution - some readdressing by brianjn)

Horizontal equilibrium = the plane of the circular plate is perpindicular to the support? (and still on the support)

If so, I still think I have a mental block against what you are asking.

Overall, I think I just don't really understand why the scale has to be in equilibrium at the end of the weighing. Isn't the point of most of these problems for the scale to be not in equilibrium?

If you place them symmetrically (ie if along the circumference, then equally spaced) then it can't be in equilibrium (similar to Charlie's logic) If there's a heavy coin, that side will weigh down. If there's a light coin, that side will go up (and the opposite side will go down), thus not ending in equilibrium.

If they are put in a nonsymmetrical fashion (ie not equal spacing, or some are closer in), then you have no guarantee that when you place them the first time, they will be in equilibrium.

Posted by Gamer on 2008-03-25 22:46:08