Grouping puzzle: 12 people, split into 4 groups of 3

I got this math question a few days ago and have been struggling to figure it out. Here it is:

Imagine that you have 12 people: A, B, C, D, E, F, G, H, I, J, K, and L. You split them into four groups of three. After you have done that, you separate them. Then you put them into four more groups of three, but this time none of the twelve people can be in a group with anyone they have already been in a group with. You keep repeating this process.
Here are the two questions:
1. How many times can you repeat the above process before it is impossible to group the twelve people again without at least one person being grouped with someone they have already been with?
2. What are the exact group arrangements for this?
For the first question I answered "five rounds", my logic being that each person has eleven other people to group with. However, they can only group five times before they must group with the one remaining person, plus someone they have already grouped with.
I have been working on the second question for a few days but haven't been able to find the answer.

Thank you for reading this, and hopefully you have an answer!

(I made this more brief than I should have; my browser crashed during my first attempt and I had to restart. Be sure to reply to this post pointing out anything I may have left out.)

EDIT: for question two, you have to list all grouping arrangements for all grouping rounds. For example, if you answered "2 rounds" for the first question, you would then have to list those two rounds, e.g. Round 1 - [A,B,C / D,E,F / G,H,I / J,K,L]; Round 2 - [A,G,J / D,H,K / B,E,L / C,F,I]

Paxo8 said:

I got this math question a few days ago and have been struggling to figure it out. Here it is:

Imagine that you have 12 people: A, B, C, D, E, F, G, H, I, J, K, and L. You split them into four groups of three. After you have done that, you separate them. Then you put them into four more groups of three, but this time none of the twelve people can be in a group with anyone they have already been in a group with. You keep repeating this process.
Here are the two questions:
1. How many times can you repeat the above process before it is impossible to group the twelve people again without at least one person being grouped with someone they have already been with?
2. What are the exact group arrangements for this?
For the first question I answered "five times", my logic being that each person has eleven other people to group with. However, they can only group five times before they must group with the one remaining person, plus someone they have already grouped with.
I have been working on the second question for a few days but haven't been able to find the answer.

Thank you for reading this, and hopefully you have an answer!

(I made this more brief than I should have; my browser crashed during my first attempt and I had to restart. Be sure to reply to this post pointing out anything I may have left out.)

Click to expand...

Since you have to have the exact group arrangements, why don't you start with that in a systematic way. For example start with A and you get the five you mentioned:
(A, B, C), (A, D, E), (A, F, G), (A, H, I), (A, J, K). Of course, you could have swapped out any one with the L but that would still only leave 5 groups. So, is that what you mean or would you want to include, for example, (L, B, D) for number six where B and D have been used before but not together.

Ishuda said:

Since you have to have the exact group arrangements, why don't you start with that in a systematic way. For example start with A and you get the five you mentioned:
(A, B, C), (A, D, E), (A, F, G), (A, H, I), (A, J, K). Of course, you could have swapped out any one with the L but that would still only leave 5 groups. So, is that what you mean or would you want to include, for example, (L, B, D) for number six where B and D have been used before but not together.

Click to expand...

Not exactly. To get the answer, I need to have all the group arrangements for all five rounds of grouping (if it really is five).

So, for example, the first of the five rounds could be [A/B/C, D/E/F, G/H/I, J/K/L].
Then the second round could be [A/D/G, J/B/E, H/C/K, F/I/L].
After that, I would have to figure out the third, fourth, and fifth rounds.

bump after 4 years!

Did Paxo8 or anyone else figure this out?
I have the exact same problem and found this forum.

12 people into 4 groups of 3 members.
How many groups can I make so that every group is a completely new one?
And what are the exact arrangements for the groups for each round?