IMP POW 1: The Broken Eggs
Problem Statement:
A farmer’s cart hits a pothole, causing all her eggs to fall out and break. Luckily, she is unhurt. To cover the cost of the eggs, her insurance agent needs to know how many she had. She can’t remember the number, but can remember some problems she had when packing the eggs. When she put the eggs in groups of two to six eggs, there was always one left over. However, in groups of seven, there were none left over. From what she knows, how can she figure out how many eggs she had?

Process:
First, I thought the answer would be forty-nine. Then, I realized my mistake and tried to think of different ways to do it. I decided to make a chart showing the remainders of the numbers two to six into multiples of seven. I then started to find a pattern. I noticed that the number two has a remainder of one every other multiple of seven, the number three has a remainder of one every two multiples, the number four has a remainder of one every three multiples, and so on. I marked a dot every time there was a remainder of one. I knew that when I had dots marked from two through seven, that would be the answer. So I set out on the long journey of calculating when there was a remainder of one until I reached a number that was all filled up.

Solution:
Using my process, I found that the number of eggs the farmer had was three-hundred one. I know this because it was the first number to fit my boundaries. This number, when put in groups of two to six, will have a remainder of one, but when put in groups of seven, will magically have no remainder. I can assume that there would be another possible larger number that would work, but unfortunately I was too lazy efficient to calculate it.

Evaluation:
Trying to figure out how to solve this problem was very hard. However, once I knew how, it was easier. I think this problem definitely benefited me. I learned that no matter how hard a problem looks. You can always almost solve it. I...

... 09-17-10
Period 5
The BrokenEggsPOW #11. Problem Statement:
A farmer has some eggs in a cart, and is going to market them. She accidently breaks every egg. She doesn’t remember how many she had, but she remembers some things. She knows that when she put them in groups of 2, 3, 4, 5 and 6, there was one egg left over. When she put them in groups...

...1. To find my conclusions I had to think about each part of the problem. When you know that one thing means you go on to the next part. When you figure out what that means you have to see how the two statements are related. If they are related then you can deduce a conclusion that makes sense.
2. Here are my conclusions for the 6 problems on page 7.
1. a. No medicine is nice
b. Senna is a medicine
Here I deduced that Senna is not a nice...

...“A Sticky Gum Problem” POW 4
Problem statement:
The next scenario is very similar. In this one, Ms. Hernandez passed a different gumball machine the next day with three different colors Once again her twins each want a gumball of the same color, and each gumball is still one cent. What is the most amount of money that Ms. Hernandez would have to spend in order to get each of her daughters the same color gumball?
In the last scenario, Mr. Hodges and his triplets pass...

...Mega POW
A very wealthy king has 8 bags of gold, which he trusts to some of his caretakers. All the bags have equal weight and contain the same amount of gold, all the gold in the kingdom. Although, the king heard a story that a woman received a gold coin. The king knew it had to be his gold so he wanted to find the lightest bag in the 3 weighing, but the mathematician thought it could be done in less, so I need to find out the least amount of weighing it takes to find the...

...probability using both an experimental and theoretical model. My real goal is to find the strategy with the highest probability of success or the one most likely to help me win.
Strategy # 1
a. Always choose the same thing the card says. So if it is an O choose O, if it is an X choose X.
b. 30 trials
1. yes 6.no 11.no 16.yes 21.yes 26. yes
2. yes 7.yes 12.yes 17.yes 22.no 27. yes
3. yes 8.no 13.yes...

...POW (BrokenEggs)
A farmer is taking her eggs to the market when her cart tips over shattering all of the eggs. She goes to an insurance agent unsure of how many there actually were. She needs to know this to tell the agent though. However, she does know that when she put the eggs in groups of two, there would be one left over. This also seemed to be true for groups of three, four, five, and six. But when...

...Name: Modella Studente POW # 1BrokenEggs
Problem Statement: How many eggs were broken? (And is there more than one answer?)
Process: Given that she lined them up by twos and one was left over, by threes and one was left over, by fours and one was left over, by fives and one was left over, by sixes and one was left over and by sevens and it came out evenly, we figure the number had to be a multiple...

...Problem Statement:
Some families didn’t want to travel overland to California so they took ships around Cape Horn at the tip of South America. Say a ship leaves San Francisco for New York the first of every month at noon. At the same time a ship leaves New York for san Francisco. Every ship arrives exactly 6 months after it leaves.
If you were going to San Francisco from New York How many ships from San Francisco would you meet?
I assumed that entering and exiting the harbor does not...