I have to group a list of people into pairs and I want to know all the possible arrangements.?

Question

They all have to be paired and the people cannot be matched up with the same person twice. Is someone able to create an algorithm for this? Online or executable would be great! (Or if anyone knows of an existing program that will do this and where I can download it?)

They all have to be paired and the people cannot be matched up with the same person twice. Is someone able to create an algorithm for this? Online or executable would be great! (Or if anyone knows of an existing program that will do this and where I can download it?)

In fact in this case the number of people is 14. It seems that it is actually impossible to do this when the number of people is not a multiple of four - is it solvable?

Sorry... I wasn't clear enough... I need 14 arrangements so that no two people are ever paired with the same person twice. I think this is impossible.

Answer 1

Normally, math types would say:
There are 14 choices for the 1st member of any pair
There are 13 choices for the 2nd member.
The total possible # of choices is 14 times 13 = 182

It sounds like you have some other constraint, but you're not telling us what it is.

Answer 2

The problem is solvable whether or not the number of members in the group is a multiple of 4. As CD indicates, if there are n members in the group, there are n choices for the first and n - 1 choices for the second, so n*(n-1) . This is the number of ways to choose 2 if you count the pair (a,b) as different from (b,a). Without regard to order, there are
n*(n - 1)/2 ways.

Answer 3

Let's represent each person from A to N, that's 14 in all.

Lets pair them this way that each may be paired 13 times.
AB, AC, AD, AE, AF, AG, AH, AI, AJ, AK, AL, AM, AN
BC, BD, BE, BF, BG, BH, BI, BJ, BK, BL, BM, BN
CD, CE, CF, CG, CH, CI, CJ, CK, CL, CM, CN
DE, DF, DG, DH, DI, DJ, DK, DL, DM, DN
EF, EF, EH, EI, EJ, EK, EL, EM, EN
FG, FH, FI, FJ, FK, FL, FM, FN
GH, GI, GJ, GK, GL, GM, GN
HI, HJ, HK, HL, HM, HN
IJ, IK, IL, IM, IN
JK, JL, JM, JN
KL, KM, KN
LM, LN
MN

See if this is what you mean. If we can do it manually at least you may have an idea how to automate it. You may check by making a tally board that each of them is paired 13 times without repetition in any pairings.

Answer 4

if you have 14 people then the answer is 14 x 14 = 196.