rainbow@ihuxe.UUCP (05/31/84)
problem:12 coins, one counterfeit. Determine which it is and if its heavier
or lighter. One balance is at your disposal to be used three times.
solution:weigh four vs four, two possibilities.
A:balance, meaning there are now four coins one of which is counterfeit.
1)weigh three of them vs 3 good coins(from other pile of 8)
a.if they balance the odd coin can easily be tested with the last weighing.
b.otherwise weigh one of the three against another. Since we know whether
the counterfeit coin is light or heavy, it can be isolated.
B:imbalance, leaving a pile of 4 light coins and 4 heavy coins.
1)take two light coins,two heavy coins and weigh them against 2 good coins
and 1 light coin and 1 heavy coin.
a.Left side heavy means the counterfeit coin is among the two heavy on
the left or the light one on the right. Weigh the two heavy ones to
isolate counterfeit coin.
b.Right side heavy means the counterfeit coin is among the two light on
the left or the heavy one on the right. Weigh the two light ones to
isolate counterfeit coin.
c.Balance means the counterfeit coin is among the third pile. One heavy
or one light. Weigh either one vs a good one to isolate.