How do I create a schedule for n-pastors visiting n-churches?

Question

I want to make a schedule for many pastors. The conditions are:

1. Every month, each pastor must must go to another church,
2. The pastor must not go to same church where he came
3. In 1 year he must go to 12 different churches
4. There is 13 churches and 13 pastors and every church accepts only 1 pastor every month

I can't use random(1 to 12) because there is a chance the pastor could go to the same church (8,3% chance he goes to the same church).

I want to make the chance small (around 3% or less) that he goes to same church.

Answer 1

Your conditions don't require that the next church for a given pastor be randomly selected. Couldn't you just iterate through the church list?

That is, assign each pastor a number, 0-12. Assign each church a number, 0-12. The first month:

Month 0:
pastor-0 --> church-0
pastor-1 --> church-1
pastor-2 --> church-2
...
pastor-n --> church-n

The next month, just increment one of the counters (with wrap-around)

Month 1:
pastor-0 --> church-1
pastor-1 --> church-2
pastor-2 --> church-3
...
pastor-n --> church-0

Then repeat for the remaining months:

Month 3:
pastor-0 --> church-2
pastor-1 --> church-3
pastor-2 --> church-4
...
pastor-(n-1) --> church-0
pastor-n --> church-1

There's a very simple loop to all this (O(n)). If it's confusing to you, I suggest trying the loop on paper with say n=3.

If the randomness is a requirement then please update your question.

EDIT BY PAX

I'm deleting my answer and up-voting this one since it's O(n) and the expansion of mine to cater for the edits would have been at least O(n^2).

You can still have randomness by making the pastor-0 through pastor-N values indexes into an array of pastors that has been randomly sorted so that makes this solution at least as good as mine.

END EDIT BY PAX