Pow 2: Tying the Knots

POW 2: Tying the Knots

Problem Statement- In this imaginary land, there is a 3 stage marriage ritual that you have to complete to get married. First, the queen holds 6 strings in her first that are identical. Each string is sticking above and below the fist. Second, a person from the couple has to tie pairs of 2 together so that there are 3 pairs, and 6 strings still at the bottom. Finally, the other member of the couple comes and randomly picks 2 of the bottom strings and ties them together and repeats that until all of strings are paired together. Once all the strings are tied with a pair on both sides of the fist the queen drops all the strings to see what the outcome is. If all the strings are all tied together in 1 big loop, the couple is bound to marry, but if not- the ritual must be repeated in 6 months.

Process- First I started out by figuring out how many different outcomes there could be. For example: 1 loop, 2 loops, 3 loops or more. In our class we tested this problem out with a partner and some people got 1 loop, a few got 2 and 1 group got 3 loops. Knowing that there were 3 possible outcomes, I started drawing random diagrams with the strings labeled as A, B, C, D, E, and F.

That got really confusing so I started to find a pattern to find all the individual outcomes. I realized that no matter what, you will start out with each string paired with a string next to it. Any way you look at it, each pair will be identical in the beginning. So each of my combinations doesn't really matter what the top strings are tied to due to they are all identical.

The first pair I found was A+B, C+D, and E+ F. It made 3 loops.

AB CD E F

So I recorded that outcome down on a piece of paper. Next, I put A+B and then switched the other 2 pairs of letters so it would be C+E and D+F and vice versa. After that, I put all the