In order to get out of the dungeon, you must perform a service for the king.He wants you to identify a counterfeit coin among twelve coins, but you can only use his scale three times to do it. Lucky for you, you are the kingdom's top mathematician. I can slice a tomato into 18 pieces with five cuts, but this one's a real head scratcher. Jennifer Lu sure came up with a hard one in this riddle. I might have been able to figure it out, if I had infinite time and no stress, but the scenario as it is would not allow for that. The king has a temper, you know. (via Geeks Are Sexy)
Do we know that the counterfeit coin is lighter? If so: 1 Weigh coins 1 to 4 against coins 5 to 8. If one batch is lighter, it contains the counterfeit. If they balance, then the counterfeit is one of the 4 we didn't weigh. So whatever the result, we've narrowed it down to one of 4 coins. 2 Weigh 2 of the 4 against the other 2. The lighter pair of coins contains the counterfeit. 3 Weigh that pair against each other. The lighter one is counterfeit.
Do we know that the counterfeit coin is lighter? If so:
ReplyDelete1 Weigh coins 1 to 4 against coins 5 to 8. If one batch is lighter, it contains the counterfeit. If they balance, then the counterfeit is one of the 4 we didn't weigh. So whatever the result, we've narrowed it down to one of 4 coins.
2 Weigh 2 of the 4 against the other 2. The lighter pair of coins contains the counterfeit.
3 Weigh that pair against each other. The lighter one is counterfeit.