The person whose bag was lighter than the others would clearly be the cheat. Develop a scheme for comparing bags that will always find the light one. I know there is no scheme with fewer weighings that will work because there is no other way to narrow eight down in smaller groupings.

Develop a scheme for comparing bags that will always find the light one. 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. One of the people the king trusted did steal, so one of the bags is going to weigh less.

On special occasions he asked them to bring the bags back so he could look at them. If you think that the king cannot find the lighter bag in fewer than three weighings, prove it. He told me a way that was very similar to the way I grouped them.

His court mathematician thought that it could be done in fewer weighings.

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. Describe how you found your answer and how you convinced yourself that your method works in all situations.

Explain how you know that there is no scheme with fewer weighings that will work. 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.

Powered by Create your own unique website with customizable templates. What do you think? If the king wants to use the pan balance as few times as possible, then he will have to use it three times.

I had two groups of four, and four of two. If you have eight bags, first you need to split in right in the middle and weigh four on one side and four on the other. The mathematician was correct! The only scale in the country was a pan balance. He thought he might have to use it three times in order to be sure which bag was lighter than the rest.

What do you think? The person whose bag was lighter than the others would clearly be the cheat. Then you weigh the last two, and the one that weighs less is the lighter bag! If you think your answer is the best possible, describe how you came to that conclusion. That group of four bags has the lighter bag.

So the king asked the eight trusted people to bring their bags of gold to him. Explain how you know that there is no scheme with fewer weighings that will work.

So the king asked the eight trusted people to bring their bags of gold to him. Explain how you can be sure that your scheme will always work. His court mathematician thought that it could be done in fewer weighings.

To answer this question, follow these steps.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. 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.

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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.

Imp 1 Pow 14 Eight Bags Of Gold. Problem Statement There are twelve items numbered 1 through 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.

One can compare the sum of the values of a number of items in a set with the sum of the values of items in a. POW # Eight Bags of Gold. 12/5/ 0 Comments Once upon a time there was a very economical 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.

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