Permutation question with a dial

In summary, the conversation discusses the problem of finding the number of ways to connect 12 numbers in a circle, and the solution of 66 possible lines by creating 6 pairs and offsetting them 11 times. The person also mentions attempting to solve the problem using factorials and refers to a video on the Enigma code for inspiration. They ask for other ways to solve the equation using the logic from the video.

Homework Statement

So, you have a dial with 12 numbers (1 through 12), and you're wondering how many ways can you connect an number to another. So its therefor asking how many lines can you make with 1 - 12 in a circle.

The Attempt at a Solution

I got the solution, I made 6 pairs one number to the one 3 numbers away from it (in a circular manner) and I knew if I were to offset everything by one id next a combination, and I could do this 11 times.

6 pairs * 11 offsets = 66 possible lines.

But I was wondering how to do this in a more mathematical manner (with factorials.) And I watched this interresting video on the enigma code "http://www.youtube.com/watch?v=G2_Q9FoD-oQ".

So I tried the same logic on the permutation the man used for the 26 letters. I attempted
12!/(6!^2 * 2^6) and didn't get 66.

How would you solve this using the logic that video used on the Engima code. I would simply like to know other ways to solve this equation

You want the number of ways of partitioning 12 things into pairs? Pick one item at random. How many ways of choosing its pair? Now pick one of the remaining 10. How many ways to choose its pair? ...

1. What is a permutation question with a dial?

A permutation question with a dial is a type of mathematical problem that involves arranging a set of items or numbers in a particular order, using a dial or wheel to create different combinations. It is often used to calculate the number of possible outcomes in a given scenario.

2. How do you solve a permutation question with a dial?

To solve a permutation question with a dial, you must first determine the number of items or numbers in the set and the number of positions on the dial. Then, use the formula nPr = n! / (n-r)! to calculate the total number of possible combinations. Finally, plug in the values and solve for the answer.

3. What is the difference between permutation and combination?

Permutation and combination are both methods of arranging a set of items or numbers, but the main difference is that permutation takes into account the order of the items, while combination does not. In other words, permutation considers arrangements where the order matters, while combination only looks at the total number of items in a set.

4. Can a permutation question with a dial have repeat numbers?

Yes, a permutation question with a dial can have repeat numbers. For example, if there are 4 numbers on the dial and you are choosing 3 numbers, the same number can be chosen more than once, resulting in different combinations. However, the formula for solving permutations with repeat numbers is slightly different.

5. How is a permutation question with a dial related to real-life situations?

Permutation questions with a dial can be used to represent many real-life situations, such as combinations on a lock, lottery numbers, or seating arrangements. It can also be applied in fields such as statistics, genetics, and computer science to calculate the number of possible outcomes or combinations in a given scenario.

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