9/12/10
IMP
POW Linear Nim
In this POW, we had to play a game called Linear Nim. In this game, we drew 10 lines on a paper, and we had to take turns crossing out 1, 2, or 3 of the marks. The person that crossed out the last mark was the winner. The first task of this POW was to find a winning strategy for this game. After we found this out, we were supposed to make variations to the game, for instance starting with more or less marks, or allowing a player to cross out more or less marks. We were supposed to consider a variety of examples and look for generalizations in strategies. When I first played the game, I didn’t really have any initial strategy in mind. I just picked numbers at random to choose until getting down to the last few. I thought this game was very simple and easy to understand. One key insight I had was to cross out three marks to get rid of most of the marks. When it came down to the final three or four marks, I had to look carefully at them to see what numbers I could choose before the next person’s turn, so after their turn there would be one, two, or three marks left. For instance, if there were 5 marks left, I could cross out one, and then any number the next person picked would leave me with a number of marks I could cross out with one, two, or three crosses. This is when I realized the strategy of this game. The strategy I developed for the original game was that to win, you have to cross out a number of marks so that there are four marks left before the next persons turn. If your opponent picks three, there will be one mark left, and you can cross it out and win. If your opponent crosses out two marks, there will be two marks left, and you can cross those out and win. If your opponent crosses out only one mark, there will be three marks left, and you can cross those out and win. If you get down to four marks before the next person’s turn, there is no possible way you can lose. At least without any variations. My first variation was...

...Taylor Gray
1/31/11
POW 6: linearnim
For this game of LinearNim you draw 10 line marks on a piece of paper and two players take turns crossing off only 1, 2, or 3 marks per turn. The person who crosses off the last mark is the winner. Firstly what I did was play a few games with my Mom and what I realized right away was that if you stopped just before the last four dashes in the game then you would always win....

...Problem statement. There’s this game called linearnim where 2 players who have 10 marks and so they have to figure out a strategy. Then who ever crosses out the last mark wins. You can also play it with 15 marks. But you have to figure what to do while playing this game and try to find patterns or strategies to win.
Process. So what I did to attempt the problem is that I played the game a few times with my partner with the 10 marks and 15. So we can find some...

...Some Golden Retrievers are gold
These dogs are gold
3. This POW has to do with mathematics because it is all about logic. In math without logic you would less successful then if you do have logic. If something does not seem right to you or is confusing you are using logic to realize that something is wrong and will use it to solve it. Without logic you wouldn’t know when something is right or wrong.
4. This POW was fairly simple. But some of the...

...“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...

...Sage Wentzell-Brehme
Problem Statement
In this problem I am looking at strategies for a game called What’s on Back?
This game has 3 cards. One card has an X on both sides, one card has an O on both sides, and one has an O on one side and a X on the other. On your turn you choose one of the cards at random from a bag. You hold it up with one side facing you. You are not allowed to look at the other side or the other cards. You have to predict whether it is an O or an X on the other...

...Problem Statement: A football league scores points for field goals as five points and touchdowns as three points. They want to know what the highest amount of points that is impossible to score.
Process: I thought that maybe there was patterns in certain combinations.
Field goals = 5 pts. Then I listed the multiples of 5 to 25.
5,10,15,20,25
Touchdowns = 3 pts. I did the same as above.
3,6,9,12,15,18,21,24,27
I looked at the patterns and knew that if the team only scored field...

...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...

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