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: Minimum? by brianjn)

Since there is no such thing as perpetual motion, it has to come to equilibrium even if the scale is out of balance.  Something will stop it and it will be in equilibrium. Hopefully the pivot in the center doesn't allow the disk to fall completely off, but regardless of what sort of equilibrium is achieved, either with the disk almost vertical or having fallen off onto the table in a particular direction, equilibrium will have been achieved.

Posted by Charlie on 2008-03-21 09:22:15