Eight Bags of Gold Pow 3

POW 6-Eight Bags of Gold

Sean Dela Torre

MOT Charter

Problem Statement

Once upon a time there was a greedy king who owned all the gold in his land. He kept all the gold in eights bags. The king gave the eight bags to eight nobles whom he trusted a lot. One day he heard from an old woman that one of the nobles had given her some gold in exchange for merchandise, except she didn't quite remember who the noble was. In order for the king to find out who the untrustworthy noble was, the king decided to call all the eight nobles in and weigh their bags in a scale (pan balance), to see whose bag was lighter than the others. The king thought that he only needed to use the scale three times, however, his court mathematician thought that it could be done in fewer weightings. What do you think?

Process

I reread the document and tried to figure out a way to make a reasonable statement. After reading the problem for a second time i soon realized that back in middle school we did a problem similar to this. To get started on this problem i used coins to help me get a better understanding of what i was doing. (just pretend the coins are bags)

Solution

Put four bags(coins) in each of the pans. Now let's say that the bags(coins) in the left are lighter than the ones in the right. All you have to do now is take the four bags in the left and put two of them in one pan