Problem Statement: A couple wants to get married but to do so a ritual must be completed. This ritual includes 6 strings. The ends of each of these strings must be tied to one another on both ends. If the strings make one large loop they can get married, anything else however will result in them having to wait.
The problem is whether or not they will get married. The best way to find this answer is to find combinations of different loops. Then find the probability of getting only one big loop. Then find the probability for all other combinations.
Process: When I first read the problem I began to think that there would only be 3 combinations for all of the strings together. Once I began to work it out then I real
...ized that the top strings don't even matter, because no matter how you start out it is random and the bottom ones haven't been tied. So now that I only had the bottom ones to work with it was a lot easier to figure out. After a while, I found that there were three circles for the strings and started to work them out.
To keep track of my results I listed them below and would number the combinations starting at one so I knew which would work. I did this until I came up with my chances and used them for my final answer. 1+4 2+3 5+6=no-2 1+4 2+6 5+3=1 1+4 2+5 6+3=1 1+5 2+3 4+6=1 1+5 2+4 3+6=1 1+5 2+6 3+4=no-2 1+6 2+3 4+5=1 1+6 2+5 4+3=no-2 1+6 2+4 5+3=1 1+2 3+4 5+6=no-3 1+2 3+5 4+6=no-2 1+2 3+6 4+5=no-2 1+3 2+4 5+6=no-
1+3 2+5 4+6=1 1+3 2+6 5+4=1 Solution: answer (they have an 8/15 chance of getting wed which is a little over 50%) because 8 out of the 15 possible outcomes made one big loop. They have a 1/15 chance to get 3 loops and a 6/15 chance of having one big loop and one small total outcome 15. If you want to get 1big loop then your chances are 8/15. If you wanted 2 loops then you have 6/15 chance of happening. The loner loops are 3 with only 1/15 chance of happening. I found these answers from my diagrams and from the answers listed above. All of the loops have different chances because you must do a different combination of tying them to get that certain loop.
For some of the loops the combination was more difficult to get and came up less when working it out giving them what chances they received. Solution
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