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.