## Exhibition Reflection-

What pow did you do?

My group did pow number eight, the “Economical King” which was about a king who possessed eight bags of gold(all of which weighed equally). Now, one of the bags of gold had less gold than the others; and the king wants to find out which, but by taking the least amount of weighings to figure out which bag is the lightest. Our job was to find out that number.

What did you do to present the pow?

My group and I went about presenting this pow by putting four pieces of chocolate into eight paper bags. Only one of the bags contained less chocolate than the others.Then, we put the bags on a scale and made the audience figure out which side side weighed less; and continue to do so until they got to the lightest bag. Then, from then on continue to find less and less ways to weigh the bags until they got the least amount of ways to do so.

How did presenting the pow the pow improve your understanding of the pow?

Presenting this pow for me improved on my understanding of the pow because I felt that I got different ways to solve the pow using different methods, this was because I worked with many different people on the same pow. All of which did the pow with different techniques.

## The Cookies Project-

Cover Letter- Haley Benjamin

During this unit, I learned lots of new skill such and graphing inequalities and solving different types of algebra like the “Two solutions” homework. From this unit I both mastered skills I had done last year as well as learned new skills. Also, I kept all my works neat and clean and in its’ own folder which for me made it easier to understand. For our main problem that we solved over this unit was trying to solve a maximum number of cookies that can be sold but at the same time keeping within the limits that we had such as dough, time, space, and icing; by finding inequalities and feasible regions. Lastly, I feel like I developed a great amount during this unit because of the amount of new skills I took in, even if I don’t understand them all yet, I still had time to be introduced them.

During this unit, I learned lots of new skill such and graphing inequalities and solving different types of algebra like the “Two solutions” homework. From this unit I both mastered skills I had done last year as well as learned new skills. Also, I kept all my works neat and clean and in its’ own folder which for me made it easier to understand. For our main problem that we solved over this unit was trying to solve a maximum number of cookies that can be sold but at the same time keeping within the limits that we had such as dough, time, space, and icing; by finding inequalities and feasible regions. Lastly, I feel like I developed a great amount during this unit because of the amount of new skills I took in, even if I don’t understand them all yet, I still had time to be introduced them.

Pow- Nim

The pow that I am going to present this semester is the "Nim" pow. For this pow the problem was for the game Nim, you start with ten lines and each player can take turns crossing off either 1, 2, or 3 of the marks; then the player who crosses off the last mark is the winner. My job was to figure out was if there was a way to win every time with a particular strategy. Then once that was found we had to figure out how to win every time if there were more than 10 lines and each player was able to take off for than 3 lines at a time. So, for the original game, in order to always win, there would have to be 4 lines left, because then no matter how many lines the other person takes off you’d win; and that rule will carry on for any amount of lines. Then, it got a lot harder when we thought about if each player was able to take more than 1, 2, or 3 lines. So, we came to the realization that if you took away 8 lines then you’d win. And that would work with any amount of lines that each player could take away. One of the generalizations that we came upon was that to win, you would always have to take away 2 lines to start. But, this only works for the rule that you can only take away 3 lines max, but there can be as many lines as you want. As, a result, in order to always win you’d have to have one number amount above the amount you’re allowed to take away. Hence, if can take away a max of seven, you’d have to take away 8 lines to win, or if you could take away 10 as a max, you’d have to be at 11 lines to win.

The pow that I am going to present this semester is the "Nim" pow. For this pow the problem was for the game Nim, you start with ten lines and each player can take turns crossing off either 1, 2, or 3 of the marks; then the player who crosses off the last mark is the winner. My job was to figure out was if there was a way to win every time with a particular strategy. Then once that was found we had to figure out how to win every time if there were more than 10 lines and each player was able to take off for than 3 lines at a time. So, for the original game, in order to always win, there would have to be 4 lines left, because then no matter how many lines the other person takes off you’d win; and that rule will carry on for any amount of lines. Then, it got a lot harder when we thought about if each player was able to take more than 1, 2, or 3 lines. So, we came to the realization that if you took away 8 lines then you’d win. And that would work with any amount of lines that each player could take away. One of the generalizations that we came upon was that to win, you would always have to take away 2 lines to start. But, this only works for the rule that you can only take away 3 lines max, but there can be as many lines as you want. As, a result, in order to always win you’d have to have one number amount above the amount you’re allowed to take away. Hence, if can take away a max of seven, you’d have to take away 8 lines to win, or if you could take away 10 as a max, you’d have to be at 11 lines to win.