If they balance, then 1 is the different coin. Whichever side is heavy is the different coin. Now, if 1,5,6 vs 2,7,8 does not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy coin, or 1 is a different, light coin.įor the third weighing, weigh 7 against 8. The direction of the tilts can tell us whwther the offending coin is heavier or lighter. If they balance then the different coin is 3, otherwise it is 4. If they balance, then the different coin is either 3 or 4. Now, in order to proceed, we must keep track of which side is heavy for each of the following weighings. What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these coins could be the different coin. Proceed as in the step above, but the coin you're looking for is the light one. If not, the heavier one is the heavy coin. Simply weigh 9 against 10 if they balance, 11 is the heavy coin. In this case, you know that the different coin is 9, 10, or 11, and that that coin is heavy. (1) They balance, in which case you know 12 is the different coin, and you just weigh it against any other to determine whether it is heavy or light. So for our second one possibility is to weigh 9,10,11 against 1,2,3 If they balance, then the different coin is in the group 9,10,11,12. For the first weighing let us put on the left pan coins 1,2,3,4 and on the right pan coins 5,6,7,8. So that the following plan can be followed, let us number the coins from 1 to 12.
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