My wife is being asked to come up with a "Prayer Partner" list, containing 12 women, who pray over the course of 11 weeks, each one partnered with the other only once. Person 1 is the "Leader" of the group. I have matched Person 1 to each person in the group once. Row 1 has the prayer partner. Column 3 starts the matching at Row 2 (first week):

I cannot figure out a way to complete the pattern. Basically, if Person 1 is assigned to pray with person 2 in week 1, person 2 needs to be assigned to person 1 in week 1, and so forth. In the above, I have person 1 assigned to each prayer partner in turn, and consequently, each person assigned to person 1 in the appropriate week.

Will someone please help me?

DrU

You have 12 people and 11 weeks. If they pray in pairs you have 6 pairs for each week. Start with setting up prayer partners for person 1.

person 1 prays with person 2 first, and in the next weeks proceeds to take turns with each other person. That looks like this:

Notice how I filled in the first column as well. Underneath Person1 there is the Person number they are paired with in each week. In the first row you can see the numbers 2 and 1. Let's fill in the rest of the row with the other ten numbers.

shot2.png

3 pairs with 12 and 12 pairs with 3. Works out just fine.

Let's fill in the same pattern for the remaining weeks, following the diagonal line of P1. Note that in some cases people would be paired with themselves, so we remove the value. These cells are highlighted in yellow.

Fill in the start of the rows to complete the patterns and remove the numbers in cells where people are paired with themselves.

In week 2 we now see empty cells for P2 and P8, so we just pair these two. Similarly in week 4 we pair P3 with P9 and so on.

And that's it. Every person paired with every other person only once.

cheers, teylyn