If you think your answer is the best possible, describe how you came to that conclusion. Once again, whatever side that weighs the least will have the bag with less gold. Next, split up the remaining four.
I read over the problem a couple times to make sure I had a clear vision of the situation in my head because I really wanted to make sure I understood what the problem was asking.
He told me a way that was very similar to the way I grouped them. Develop a scheme for comparing bags that will always find the light one. If you think that the king cannot find the lighter bag in fewer than three weighings, prove it.
Then you weigh the last two, and the one that weighs less is the lighter bag! The mathematician was correct! The pan balance has two on one side, and two on the other.
So the king asked the eight trusted people to bring their bags of gold to him. The only scale in the country was a pan balance. I prefer problems where I am thinking and then I slowly get the correct answer instead of just saying "Oh it works like this okay I get it. He thought he might have to use it three times in order to be sure which bag was lighter than the rest.
He thought he might have to use it three times in order to be sure which bag was lighter than the rest. Powered by Create your own unique website with customizable templates.
Then write a proof that your method will work in every situation. Since the king owned all of the gold in his country, it was obvious that one of the eight people he trusted was cheating him. I had two groups of four, and four of two. Explain how you know that there is no scheme with fewer weighings that will work.
Explain how you know that there is no scheme with fewer weighings that will work. Explain how you can be sure that your scheme will always work. On special occasions he asked them to bring the bags back so he could look at them. What do you think? Describe how you found your answer and how you convinced yourself that your method works in all situations.
The king wanted to use the pan balance as few times as possible. The king then chose the eight people in his country whom he trusted the most, and gave a bag of gold to each of them to keep safe for him.
His court mathematician thought that it could be done in fewer weighings. He made sure that each bag weighed exactly the same amount.
One side on the pan balance will indicate which group of four bags weighs the least.
If the king wants to use the pan balance as few times as possible, then he will have to use it three times. The only scale in the country was a pan balance.11/15/09 Class G Lauren McCarthy Pow 3: Eight Bags of Gold Problem Statement A king divides his gold among 8 trusted people.
One of the trusted people is selling his gold. The king wants to find the thief but only has a pan balance. All of the values or "weights" are the same except one item whose value is either greater than or less that the other 11 by an unknown amount. This was overlooked in the last POW (Eight Bags of Gold).
Nine items can be weighed by dividing into three sets of size three. Mega POW A very wealthy king has 8 bags of gold. Scoring Sheet for POW Eight Bags of Gold 1.
PROBLEM STATEMENT (6 pts) Max Score Score a. Restate the story of the POW in your own words 4 b. POW # eight bags of gold. 12/12/ 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.
May 20, · What is the answer to Pow 14, eight bags of gold? Upload failed. Please upload a file larger than x pixels; We are experiencing some problems, please try Status: Resolved.
Eight Bags of Gold Problem Statement: There was a king who gathered up all the gold in his land and put it into eight bags. He made sure that each bag weighed exactly the same amount.
The king then chose eight people in his country whom he trusted the most, and gave a bag of gold to each of them to keep safe for him.Download