Number of pairs that can be made with X elements without repeating a pair?

Question

I would like to make pairs out of X number of database objects.

Order of pairs does not matter.
Pairs will be made over multiple rounds.
I do not want pairs to be repeated in a subsequent round.

If I have:

A
B
C
D

The first round might be:

AB
CD

Second round might be:

AD
CB

Third round might be:

AC
DB

And there would be no other possibilities.

So for 4 elements, I could do 3 rounds before I have to repeat a pair.

What is the formula to help me with this for any number of elements?

Related How do I get the total number of unique pairs of a set in the database?

You only want to create two unique pairs per round? Edit: Sorry, after thinking about it it was a stupid question — dscham, Nov 17 '17 at 19:19
you only want, non repeating, unique pairs, so `AB` and `BA` would count as the same? — dscham, Nov 17 '17 at 19:24

score 0 · Accepted Answer · answered Nov 17 '17 at 19:38

You can use round-robin tournament algorithm to generate all possible pairs. Your example shows r-r algo in action: make two rows of elements, fix the first one (A) and rotate other elements in cyclic manner.

Note that N elements form N*(N-1)/2 pairs, and (N-1) rounds are needed to generate all of them

Number of pairs that can be made with X elements without repeating a pair?

1 Answers1