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The Fallen Ange

10-22-2004, 07:40 AM

Ok there are 12 coins in total...(No I am not giving them to you !!! )

Out of these 12 coins,11 coins have the exact same weight,while the reaming 1 coin has a different weight.We do not know if that coin is heavier or lighter.

Using a balance only 3 times tell me how you can find out the odd coin out.

lsgworldl

10-22-2004, 09:54 AM

let us number the coins from 1 to 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. There are two possibilities. Either they balance, or they don't. If they balance, then the good coin is in the group 9,10,11,12. So for our second weighing we would put 1,2 in the left pan and 9,10 on the right. If these balance then the good coin is either 11 or 12. Weigh coin 1 against 11. If they balance, the good coin is number 12. If they do not balance, then 11 is the good coin. If 1,2 vs 9,10 do not balance, then the good coin is either 9 or 10. Again, weigh 1 against 9. If they balance, the good coin is number 10, otherwise it is number 9. That was the easy part. 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 safe coin. Now, in order to proceed, we must keep track of which side is heavy for each of the following weighings. Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against 2,7,8. If they balance, then the good coin is either 3 or 4. Weigh 4 against 9, a known bad coin. If they balance then the good coin is 3, otherwise it is 4. 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 good, heavy coin, or 1 is a good, light coin. For the third weighing, weigh 7 against 8. Whichever side is heavy is the good coin. If they balance, then 1 is the good coin. Should the weighing of 1,5, 6 vs 2,7,8 show 1,5,6 to be the heavy side, then either 5 or 6 is a good heavy coin or 2 is a light good coin. Weigh 5 against 6. The heavier one is the good coin. If they balance, then 2 is a good light coin.