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Home > Logic > Weights and Scales
Circular Balance (Posted on 2008-03-20) Difficulty: 3 of 5
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.]

See The Solution Submitted by brianjn    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution part 1 solution | Comment 1 of 22

Of course it can be done with only two pans, in the classical way, with three weighings needed, as described for 11 coins at http://perplexus.info/show.php?pid=40&op=sol.

But with the circular pan it could be done in one weighing: place them equally spaced around the disk. If it tips so that one coin is at the lowest point on the circumference, that coin is the heavy coin.  If, however, one of the coins is at the highest point on the circumference, that coin is the light coin.  Since there are an odd number of coins, there won't be a coin at both the high and low points.

Edited on March 20, 2008, 12:25 pm
  Posted by Charlie on 2008-03-20 12:24:39

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