Every possible combination in a specific order

Question

all out of ideas so looking for help. So I have two tables with a single column with ID's 1-29, each ID represents a coworker. I have a 3rd table where I have already created every combination of records from the first 2 tables.

The part that I am struggling with is that I need to order my 3rd tables as follows, say person 1 calls person 2, the ID in table 3 will look like this: '1-2', now I need to make the next record start with 2 and have person 2 call someone who is not person 1 (who has already been called) and have person 1 not be called again until the remaining 28 people are already called as to ensure that everyone gets called at least once before looking through to other combos.

It's a bit hard to explain so I am willing to elaborate if needed.

For those wondering, the purpose of this exercise to to create a bit of "call train" to have everyone check up on everyone else. Thanks in advance!

Answer 1

You could set up the call chain as follows:

So in Stage 2 1 would call 3 and 2 would call 4 at the same time,etc. At each stage the number of callers would be double the number of callers from the previous stage.

(it is possible to map this into a tree structure)

EDIT#1:

I generated the pattern with this small VBA macro:

Sub Peak()
    Dim stage As Long, i As Long, j As Long, K As Long

    K = 1
    j = 1

    For stage = 1 To 5
        For i = 1 To j
            Cells(K, 1) = i
            Cells(K, 2) = K + 1
            K = K + 1
        Next i
        j = j * 2
    Next stage
End Sub

But a formula-based solution should also be possible.

EDIT#2:

In A1 enter 1
in B1 enter 2

In A2 enter:

=IF(ROWS($1:2)=2*A1,1,1+A1)  and copy downwards.

In B2 enter:

=B1+1 and copy downwards

Answer 2

It turns out that 29 is really good for this because it is prime.

What you do is have each call the next on the first cycle, then each call with a gap of 2 on the second, then a gap of 3, and so on. That results in this pattern:

1 2 ... 29
1 3 5 ... 28
1 4 8 ... 27
.
.
.
1 29 28 ... 2

And you have your 28 call trains, using each possible call only once.

Therefore the first record is 1-2. The second record is 2-3 and so on. Until the 29th record is 29-1. Then we start gaps of 2 to get 1-3 and so on.

We can even figure out a formula for that.

In general the nth record is going to be in the i = 1 + (n div 29)th cycle. (I'm using PostgreSQL SQL operators here. div means "division and drop the fraction".) It is the j = (n mod 29)th entry in that cycle (mod means the remainder after integer division). Which means that the call starts at (1 + (j-1)*i) mod 29 and goes to (1 + j*i) mod 29.