You are given nine coins. The coins are identical in all respects except that one is slightly heavier than the remaining eight. You also have a somewhat unreliable comparison (or, balance) scale. The scale may give up to one false reading, i.e., the scale may work perfectly every time, or it may produce just one erroneous result. The only possible erroneous results are either (1) indicating an inequality in either direction when, in fact, the two sides are balanced, or (2) indicating equality when the right side is heavier.

Define a procedure for identifying the heavy coin with three weighings. The procedure must also determine which, if any, of the weighings were erroneous.

(In reply to Solution by Brian Smith)

After having stepped through the solution, I see FrankM's unreliable scale is not so unreliable. 

By placing the suspected heavier coin (assuming if we received two accurate readings) on the left-side, we could not get a false reading as the scale would only show a false reading of a balance if the right-side was heavier.  If our heavier coin was not the one we have suspected, then we have already received a false reading, therefore our final reading must be accurate.  Thus it will only take three weighings to find the heavier coin.  And by knowing which coin is heavier, we can deduce which of the prior two weighings, if any, were false.

Edited on March 1, 2008, 8:31 am

Posted by Dej Mar on 2008-03-01 04:42:59