Case 4 Pow 1 Count The 8 Bags Of Gold
POW 14 Christopher Manahan Period 05
February 28, 2006
Problem Statement: A very wealthy king has 8 bags of gold- all the gold in the kingdom, which he trusts to 8 of his most trustworthy caretakers; one bag to each caretaker. All the bags have equal weight and contain the same amount of gold, totaling all the gold in the kingdom. But one day, the king hears a story that a woman from another kingdom received a gold coin. The king knew it had to be his gold, because he owned all the gold in the kingdom. Someone was spending his gold! So he decided to find the lightest bag of the 8 using a pan scale to weigh the bags of gold. The King expected that it would take 3 weightings to determine the lightest bag of gold, but the …show more content…
In this case you would take 2 out of the 3 bags of gold and weigh those. If the 2 you weighed are even, then the bag of gold you didn't weigh will be the bag with the missing coins.
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If the bag with the missing coins IS one of the ones you weighed, then obviously the bag with the lesser weight is the one missing coins.
Extensions: ( Don't be surprised if this sounds familiar- Russ helped me with this again. ^^) After this past predicament with the King and his gold, the king has decided to divide his gold further- into 12 bags instead of 8, so that the caretakers will have less to be tempted by. But despite this change, the king has found yet another untrustworthy caretaker for his gold- this time, the caretaker spending his money is trying to fool him as well. After spending his money, they are replacing his coins with counterfeit coins so that it appears that none of the currency was lost. After discovering this scheme through one of the subjects of a sister kingdom who had gotten hold of one of these counterfeit coins, the king decides once again to weigh his gold to find out who his traitor
February 28, 2006
Problem Statement: A very wealthy king has 8 bags of gold- all the gold in the kingdom, which he trusts to 8 of his most trustworthy caretakers; one bag to each caretaker. All the bags have equal weight and contain the same amount of gold, totaling all the gold in the kingdom. But one day, the king hears a story that a woman from another kingdom received a gold coin. The king knew it had to be his gold, because he owned all the gold in the kingdom. Someone was spending his gold! So he decided to find the lightest bag of the 8 using a pan scale to weigh the bags of gold. The King expected that it would take 3 weightings to determine the lightest bag of gold, but the …show more content…
In this case you would take 2 out of the 3 bags of gold and weigh those. If the 2 you weighed are even, then the bag of gold you didn't weigh will be the bag with the missing coins.
1 1
1
If the bag with the missing coins IS one of the ones you weighed, then obviously the bag with the lesser weight is the one missing coins.
Extensions: ( Don't be surprised if this sounds familiar- Russ helped me with this again. ^^) After this past predicament with the King and his gold, the king has decided to divide his gold further- into 12 bags instead of 8, so that the caretakers will have less to be tempted by. But despite this change, the king has found yet another untrustworthy caretaker for his gold- this time, the caretaker spending his money is trying to fool him as well. After spending his money, they are replacing his coins with counterfeit coins so that it appears that none of the currency was lost. After discovering this scheme through one of the subjects of a sister kingdom who had gotten hold of one of these counterfeit coins, the king decides once again to weigh his gold to find out who his traitor