# How to determine combinations of a setOctober 11, 2005 3:03 AM   Subscribe

I have a group of eight people. Sue, Jim, Pat, Don, Bob, Joe, Liz, Ned. I need to get a list of all the possible groups, sized 1 - 6, which could make from these people, while observing a few rules.

1. Bob and Joe cannot be in the same group.

2. Liz and Ned cannot be in the same group.

3. Order does not matter.

4. Groups can be as small as one and as large as six (The rules wont allow groups of 7 or 8)

VB code would be great as would any other way which would result in a printed list. I only need to do this once but it would might be useful to have the algorithm for reference.
posted by kenaman to Computers & Internet (21 answers total)

my naive prolog abilities (never really used it until trying to answer this question) suggest the following should work. it doesn't, but i've sent an email to a friend asking why - hopefully it can be fixed.

order(sue,jim).
order(jim,pat).
order(pat,don).
order(don,bob).
order(bob,joe).
order(joe,liz).
order(liz,ned).
order(A,B) :- order(A,C), order(C,B).

ordered([]).
ordered([A,[]]).
ordered([A,B|C]) :- order(A,B), ordered([B|C]).

enemy(bob,joe).
enemy(liz,ned).

friends([]).
friends([A]).
friends([A,B|C]) :- not(enemy(A,B)), friends([B|C]), friends([A|C]).

short(A) :- length(A) < 7.br>
group(A) :- short(A), ordered(A), friends(A).

?group(A).
posted by andrew cooke at 4:51 AM on October 11, 2005

...length(A) < 7
without the .br>
posted by andrew cooke at 4:51 AM on October 11, 2005

ok, this does it:

short(A) :- length(A,B), B < 7.br>
someone(sue).
someone(jim).
someone(pat).
someone(don).
someone(bob).
someone(joe).
someone(liz).
someone(ned).

people([A|[]]) :- someone(A).
people([A|B]) :- short([A|B]), someone(A), people(B).

order(sue,jim).
order(jim,pat).
order(pat,don).
order(don,bob).
order(bob,joe).
order(joe,liz).
order(liz,ned).
order(A,B) :- not('='(A,B)), order(A,C), order(C,B).

ordered([]).
ordered([A|[]]).
ordered([A,B|[]]) :- order(A,B).
ordered([A,B,C]) :- order(A,B), ordered([B,C]).

enemy(bob,joe).
enemy(liz,ned).
enemy(joe,bob).
enemy(ned,liz).

friends([]).
friends([A|[]]).
friends([A,B|[]]) :- not(enemy(A,B)).
friends([A,B,C]) :- not(enemy(A,B)), friends([B,C]), friends([A,C]).

group(A) :- people(A), ordered(A), friends(A).

(now i just need to work out how to print the results!)
posted by andrew cooke at 5:26 AM on October 11, 2005

bleagh. still not right. i give up. sorry.
posted by andrew cooke at 5:46 AM on October 11, 2005

Response by poster: Thanks very much for trying Andrew. I now feel bad in telling you that I dont know how I would have used it seeing as it is in Prolog. If no one else sorts it for me I will mark yours as the best answer.
posted by kenaman at 5:49 AM on October 11, 2005

I agree with Andrew Cooke, prolog is right programming language for this task. However, I don't have a prolog interpreter installed on my machine and it only took a few mintues to code up a working solution in perl, so I didn't bother with tracking down and installing a Mac OS X prolog interpreter.

Output of code:

Group size template: 1 1 1 1 1 1 1 1
(Bob) (Don) (Jim) (Joe) (Liz) (Ned) (Pat) (Sue)

Group size template: 2 1 1 1 1 1 1
(Bob Don) (Jim) (Joe) (Liz) (Ned) (Pat) (Sue)
(Bob Jim) (Don) (Joe) (Liz) (Ned) (Pat) (Sue)
(Bob Liz) (Don) (Jim) (Joe) (Ned) (Pat) (Sue)
(Bob Ned) (Don) (Jim) (Joe) (Liz) (Pat) (Sue)
(Bob Pat) (Don) (Jim) (Joe) (Liz) (Ned) (Sue)
(Bob Sue) (Don) (Jim) (Joe) (Liz) (Ned) (Pat)
(Bob) (Don Jim) (Joe) (Liz) (Ned) (Pat) (Sue)
(Bob) (Don Joe) (Jim) (Liz) (Ned) (Pat) (Sue)
(Bob) (Don Liz) (Jim) (Joe) (Ned) (Pat) (Sue)
(Bob) (Don Ned) (Jim) (Joe) (Liz) (Pat) (Sue)
(Bob) (Don Pat) (Jim) (Joe) (Liz) (Ned) (Sue)
(Bob) (Don Sue) (Jim) (Joe) (Liz) (Ned) (Pat)
(Bob) (Don) (Jim Joe) (Liz) (Ned) (Pat) (Sue)
(Bob) (Don) (Jim Liz) (Joe) (Ned) (Pat) (Sue)
(Bob) (Don) (Jim Ned) (Joe) (Liz) (Pat) (Sue)
(Bob) (Don) (Jim Pat) (Joe) (Liz) (Ned) (Sue)
(Bob) (Don) (Jim Sue) (Joe) (Liz) (Ned) (Pat)
(Bob) (Don) (Jim) (Joe Liz) (Ned) (Pat) (Sue)
(Bob) (Don) (Jim) (Joe Ned) (Liz) (Pat) (Sue)
(Bob) (Don) (Jim) (Joe Pat) (Liz) (Ned) (Sue)
(Bob) (Don) (Jim) (Joe Sue) (Liz) (Ned) (Pat)
(Bob) (Don) (Jim) (Joe) (Liz Pat) (Ned) (Sue)
(Bob) (Don) (Jim) (Joe) (Liz Sue) (Ned) (Pat)
(Bob) (Don) (Jim) (Joe) (Liz) (Ned Pat) (Sue)
(Bob) (Don) (Jim) (Joe) (Liz) (Ned Sue) (Pat)
(Bob) (Don) (Jim) (Joe) (Liz) (Ned) (Pat Sue)

Group size template: 3 1 1 1 1 1
(Bob Don Jim) (Joe) (Liz) (Ned) (Pat) (Sue)
(Bob Don Liz) (Jim) (Joe) (Ned) (Pat) (Sue)
(Bob Don Ned) (Jim) (Joe) (Liz) (Pat) (Sue)
(Bob Don Pat) (Jim) (Joe) (Liz) (Ned) (Sue)
(Bob Don Sue) (Jim) (Joe) (Liz) (Ned) (Pat)
(Bob Jim Liz) (Don) (Joe) (Ned) (Pat) (Sue)
(Bob Jim Ned) (Don) (Joe) (Liz) (Pat) (Sue)
(Bob Jim Pat) (Don) (Joe) (Liz) (Ned) (Sue)
(Bob Jim Sue) (Don) (Joe) (Liz) (Ned) (Pat)
(Bob Liz Pat) (Don) (Jim) (Joe) (Ned) (Sue)
(Bob Liz Sue) (Don) (Jim) (Joe) (Ned) (Pat)
(Bob Ned Pat) (Don) (Jim) (Joe) (Liz) (Sue)
(Bob Ned Sue) (Don) (Jim) (Joe) (Liz) (Pat)
(Bob Pat Sue) (Don) (Jim) (Joe) (Liz) (Ned)
(Bob) (Don Jim Joe) (Liz) (Ned) (Pat) (Sue)
(Bob) (Don Jim Liz) (Joe) (Ned) (Pat) (Sue)
(Bob) (Don Jim Ned) (Joe) (Liz) (Pat) (Sue)
(Bob) (Don Jim Pat) (Joe) (Liz) (Ned) (Sue)
(Bob) (Don Jim Sue) (Joe) (Liz) (Ned) (Pat)
(Bob) (Don Joe Liz) (Jim) (Ned) (Pat) (Sue)
(Bob) (Don Joe Ned) (Jim) (Liz) (Pat) (Sue)
(Bob) (Don Joe Pat) (Jim) (Liz) (Ned) (Sue)
(Bob) (Don Joe Sue) (Jim) (Liz) (Ned) (Pat)
(Bob) (Don Liz Pat) (Jim) (Joe) (Ned) (Sue)
(Bob) (Don Liz Sue) (Jim) (Joe) (Ned) (Pat)
(Bob) (Don Ned Pat) (Jim) (Joe) (Liz) (Sue)
(Bob) (Don Ned Sue) (Jim) (Joe) (Liz) (Pat)
(Bob) (Don Pat Sue) (Jim) (Joe) (Liz) (Ned)
(Bob) (Don) (Jim Joe Liz) (Ned) (Pat) (Sue)
(Bob) (Don) (Jim Joe Ned) (Liz) (Pat) (Sue)
(Bob) (Don) (Jim Joe Pat) (Liz) (Ned) (Sue)
(Bob) (Don) (Jim Joe Sue) (Liz) (Ned) (Pat)
(Bob) (Don) (Jim Liz Pat) (Joe) (Ned) (Sue)
(Bob) (Don) (Jim Liz Sue) (Joe) (Ned) (Pat)
(Bob) (Don) (Jim Ned Pat) (Joe) (Liz) (Sue)
(Bob) (Don) (Jim Ned Sue) (Joe) (Liz) (Pat)
(Bob) (Don) (Jim Pat Sue) (Joe) (Liz) (Ned)
(Bob) (Don) (Jim) (Joe Liz Pat) (Ned) (Sue)
(Bob) (Don) (Jim) (Joe Liz Sue) (Ned) (Pat)
(Bob) (Don) (Jim) (Joe Ned Pat) (Liz) (Sue)
(Bob) (Don) (Jim) (Joe Ned Sue) (Liz) (Pat)
(Bob) (Don) (Jim) (Joe Pat Sue) (Liz) (Ned)
(Bob) (Don) (Jim) (Joe) (Liz Pat Sue) (Ned)
(Bob) (Don) (Jim) (Joe) (Liz) (Ned Pat Sue)

Group size template: 2 2 1 1 1 1
(Bob Don) (Jim Joe) (Liz) (Ned) (Pat) (Sue)
(Bob Don) (Jim Liz) (Joe) (Ned) (Pat) (Sue)
(Bob Don) (Jim Ned) (Joe) (Liz) (Pat) (Sue)
(Bob Don) (Jim Pat) (Joe) (Liz) (Ned) (Sue)
(Bob Don) (Jim Sue) (Joe) (Liz) (Ned) (Pat)
(Bob Don) (Jim) (Joe Liz) (Ned) (Pat) (Sue)
(Bob Don) (Jim) (Joe Ned) (Liz) (Pat) (Sue)
(Bob Don) (Jim) (Joe Pat) (Liz) (Ned) (Sue)
(Bob Don) (Jim) (Joe Sue) (Liz) (Ned) (Pat)
(Bob Don) (Jim) (Joe) (Liz Pat) (Ned) (Sue)
(Bob Don) (Jim) (Joe) (Liz Sue) (Ned) (Pat)
(Bob Don) (Jim) (Joe) (Liz) (Ned Pat) (Sue)
(Bob Don) (Jim) (Joe) (Liz) (Ned Sue) (Pat)
(Bob Don) (Jim) (Joe) (Liz) (Ned) (Pat Sue)
(Bob Jim) (Don Joe) (Liz) (Ned) (Pat) (Sue)
(Bob Jim) (Don Liz) (Joe) (Ned) (Pat) (Sue)
(Bob Jim) (Don Ned) (Joe) (Liz) (Pat) (Sue)
(Bob Jim) (Don Pat) (Joe) (Liz) (Ned) (Sue)
(Bob Jim) (Don Sue) (Joe) (Liz) (Ned) (Pat)
(Bob Jim) (Don) (Joe Liz) (Ned) (Pat) (Sue)
(Bob Jim) (Don) (Joe Ned) (Liz) (Pat) (Sue)
(Bob Jim) (Don) (Joe Pat) (Liz) (Ned) (Sue)
(Bob Jim) (Don) (Joe Sue) (Liz) (Ned) (Pat)
(Bob Jim) (Don) (Joe) (Liz Pat) (Ned) (Sue)
(Bob Jim) (Don) (Joe) (Liz Sue) (Ned) (Pat)
(Bob Jim) (Don) (Joe) (Liz) (Ned Pat) (Sue)
(Bob Jim) (Don) (Joe) (Liz) (Ned Sue) (Pat)
(Bob Jim) (Don) (Joe) (Liz) (Ned) (Pat Sue)
(Bob Liz) (Don Jim) (Joe) (Ned) (Pat) (Sue)
(Bob Liz) (Don Joe) (Jim) (Ned) (Pat) (Sue)
(Bob Liz) (Don Ned) (Jim) (Joe) (Pat) (Sue)
(Bob Liz) (Don Pat) (Jim) (Joe) (Ned) (Sue)
(Bob Liz) (Don Sue) (Jim) (Joe) (Ned) (Pat)
(Bob Liz) (Don) (Jim Joe) (Ned) (Pat) (Sue)
(Bob Liz) (Don) (Jim Ned) (Joe) (Pat) (Sue)
(Bob Liz) (Don) (Jim Pat) (Joe) (Ned) (Sue)
(Bob Liz) (Don) (Jim Sue) (Joe) (Ned) (Pat)
(Bob Liz) (Don) (Jim) (Joe Ned) (Pat) (Sue)
(Bob Liz) (Don) (Jim) (Joe Pat) (Ned) (Sue)
(Bob Liz) (Don) (Jim) (Joe Sue) (Ned) (Pat)
(Bob Liz) (Don) (Jim) (Joe) (Ned Pat) (Sue)
(Bob Liz) (Don) (Jim) (Joe) (Ned Sue) (Pat)
(Bob Liz) (Don) (Jim) (Joe) (Ned) (Pat Sue)
(Bob Ned) (Don Jim) (Joe) (Liz) (Pat) (Sue)
(Bob Ned) (Don Joe) (Jim) (Liz) (Pat) (Sue)
(Bob Ned) (Don Liz) (Jim) (Joe) (Pat) (Sue)
(Bob Ned) (Don Pat) (Jim) (Joe) (Liz) (Sue)
(Bob Ned) (Don Sue) (Jim) (Joe) (Liz) (Pat)
(Bob Ned) (Don) (Jim Joe) (Liz) (Pat) (Sue)
(Bob Ned) (Don) (Jim Liz) (Joe) (Pat) (Sue)
(Bob Ned) (Don) (Jim Pat) (Joe) (Liz) (Sue)
(Bob Ned) (Don) (Jim Sue) (Joe) (Liz) (Pat)
(Bob Ned) (Don) (Jim) (Joe Liz) (Pat) (Sue)
(Bob Ned) (Don) (Jim) (Joe Pat) (Liz) (Sue)
(Bob Ned) (Don) (Jim) (Joe Sue) (Liz) (Pat)
(Bob Ned) (Don) (Jim) (Joe) (Liz Pat) (Sue)
(Bob Ned) (Don) (Jim) (Joe) (Liz Sue) (Pat)
(Bob Ned) (Don) (Jim) (Joe) (Liz) (Pat Sue)
(Bob Pat) (Don Jim) (Joe) (Liz) (Ned) (Sue)
(Bob Pat) (Don Joe) (Jim) (Liz) (Ned) (Sue)
(Bob Pat) (Don Liz) (Jim) (Joe) (Ned) (Sue)
(Bob Pat) (Don Ned) (Jim) (Joe) (Liz) (Sue)
(Bob Pat) (Don Sue) (Jim) (Joe) (Liz) (Ned)
(Bob Pat) (Don) (Jim Joe) (Liz) (Ned) (Sue)
(Bob Pat) (Don) (Jim Liz) (Joe) (Ned) (Sue)
(Bob Pat) (Don) (Jim Ned) (Joe) (Liz) (Sue)
(Bob Pat) (Don) (Jim Sue) (Joe) (Liz) (Ned)
(Bob Pat) (Don) (Jim) (Joe Liz) (Ned) (Sue)
(Bob Pat) (Don) (Jim) (Joe Ned) (Liz) (Sue)
(Bob Pat) (Don) (Jim) (Joe Sue) (Liz) (Ned)
(Bob Pat) (Don) (Jim) (Joe) (Liz Sue) (Ned)
(Bob Pat) (Don) (Jim) (Joe) (Liz) (Ned Sue)
(Bob Sue) (Don Jim) (Joe) (Liz) (Ned) (Pat)
(Bob Sue) (Don Joe) (Jim) (Liz) (Ned) (Pat)
(Bob Sue) (Don Liz) (Jim) (Joe) (Ned) (Pat)
(Bob Sue) (Don Ned) (Jim) (Joe) (Liz) (Pat)
(Bob Sue) (Don Pat) (Jim) (Joe) (Liz) (Ned)
(Bob Sue) (Don) (Jim Joe) (Liz) (Ned) (Pat)
(Bob Sue) (Don) (Jim Liz) (Joe) (Ned) (Pat)
(Bob Sue) (Don) (Jim Ned) (Joe) (Liz) (Pat)
(Bob Sue) (Don) (Jim Pat) (Joe) (Liz) (Ned)
(Bob Sue) (Don) (Jim) (Joe Liz) (Ned) (Pat)
(Bob Sue) (Don) (Jim) (Joe Ned) (Liz) (Pat)
(Bob Sue) (Don) (Jim) (Joe Pat) (Liz) (Ned)
(Bob Sue) (Don) (Jim) (Joe) (Liz Pat) (Ned)
(Bob Sue) (Don) (Jim) (Joe) (Liz) (Ned Pat)
(Bob) (Don Jim) (Joe Liz) (Ned) (Pat) (Sue)
(Bob) (Don Jim) (Joe Ned) (Liz) (Pat) (Sue)
(Bob) (Don Jim) (Joe Pat) (Liz) (Ned) (Sue)
(Bob) (Don Jim) (Joe Sue) (Liz) (Ned) (Pat)
(Bob) (Don Jim) (Joe) (Liz Pat) (Ned) (Sue)
(Bob) (Don Jim) (Joe) (Liz Sue) (Ned) (Pat)
(Bob) (Don Jim) (Joe) (Liz) (Ned Pat) (Sue)
(Bob) (Don Jim) (Joe) (Liz) (Ned Sue) (Pat)
(Bob) (Don Jim) (Joe) (Liz) (Ned) (Pat Sue)
(Bob) (Don Joe) (Jim Liz) (Ned) (Pat) (Sue)
(Bob) (Don Joe) (Jim Ned) (Liz) (Pat) (Sue)
(Bob) (Don Joe) (Jim Pat) (Liz) (Ned) (Sue)
(Bob) (Don Joe) (Jim Sue) (Liz) (Ned) (Pat)
(Bob) (Don Joe) (Jim) (Liz Pat) (Ned) (Sue)
(Bob) (Don Joe) (Jim) (Liz Sue) (Ned) (Pat)
(Bob) (Don Joe) (Jim) (Liz) (Ned Pat) (Sue)
(Bob) (Don Joe) (Jim) (Liz) (Ned Sue) (Pat)
(Bob) (Don Joe) (Jim) (Liz) (Ned) (Pat Sue)
(Bob) (Don Liz) (Jim Joe) (Ned) (Pat) (Sue)
(Bob) (Don Liz) (Jim Ned) (Joe) (Pat) (Sue)
(Bob) (Don Liz) (Jim Pat) (Joe) (Ned) (Sue)
(Bob) (Don Liz) (Jim Sue) (Joe) (Ned) (Pat)
(Bob) (Don Liz) (Jim) (Joe Ned) (Pat) (Sue)
(Bob) (Don Liz) (Jim) (Joe Pat) (Ned) (Sue)
(Bob) (Don Liz) (Jim) (Joe Sue) (Ned) (Pat)
(Bob) (Don Liz) (Jim) (Joe) (Ned Pat) (Sue)
(Bob) (Don Liz) (Jim) (Joe) (Ned Sue) (Pat)
(Bob) (Don Liz) (Jim) (Joe) (Ned) (Pat Sue)
(Bob) (Don Ned) (Jim Joe) (Liz) (Pat) (Sue)
(Bob) (Don Ned) (Jim Liz) (Joe) (Pat) (Sue)
(Bob) (Don Ned) (Jim Pat) (Joe) (Liz) (Sue)
(Bob) (Don Ned) (Jim Sue) (Joe) (Liz) (Pat)
(Bob) (Don Ned) (Jim) (Joe Liz) (Pat) (Sue)
(Bob) (Don Ned) (Jim) (Joe Pat) (Liz) (Sue)
(Bob) (Don Ned) (Jim) (Joe Sue) (Liz) (Pat)
(Bob) (Don Ned) (Jim) (Joe) (Liz Pat) (Sue)
(Bob) (Don Ned) (Jim) (Joe) (Liz Sue) (Pat)
(Bob) (Don Ned) (Jim) (Joe) (Liz) (Pat Sue)
(Bob) (Don Pat) (Jim Joe) (Liz) (Ned) (Sue)
(Bob) (Don Pat) (Jim Liz) (Joe) (Ned) (Sue)
(Bob) (Don Pat) (Jim Ned) (Joe) (Liz) (Sue)
(Bob) (Don Pat) (Jim Sue) (Joe) (Liz) (Ned)
(Bob) (Don Pat) (Jim) (Joe Liz) (Ned) (Sue)
(Bob) (Don Pat) (Jim) (Joe Ned) (Liz) (Sue)
(Bob) (Don Pat) (Jim) (Joe Sue) (Liz) (Ned)
(Bob) (Don Pat) (Jim) (Joe) (Liz Sue) (Ned)
(Bob) (Don Pat) (Jim) (Joe) (Liz) (Ned Sue)
(Bob) (Don Sue) (Jim Joe) (Liz) (Ned) (Pat)
(Bob) (Don Sue) (Jim Liz) (Joe) (Ned) (Pat)
(Bob) (Don Sue) (Jim Ned) (Joe) (Liz) (Pat)
(Bob) (Don Sue) (Jim Pat) (Joe) (Liz) (Ned)
(Bob) (Don Sue) (Jim) (Joe Liz) (Ned) (Pat)
(Bob) (Don Sue) (Jim) (Joe Ned) (Liz) (Pat)
(Bob) (Don Sue) (Jim) (Joe Pat) (Liz) (Ned)
(Bob) (Don Sue) (Jim) (Joe) (Liz Pat) (Ned)
(Bob) (Don Sue) (Jim) (Joe) (Liz) (Ned Pat)
(Bob) (Don) (Jim Joe) (Liz Pat) (Ned) (Sue)
(Bob) (Don) (Jim Joe) (Liz Sue) (Ned) (Pat)
(Bob) (Don) (Jim Joe) (Liz) (Ned Pat) (Sue)
(Bob) (Don) (Jim Joe) (Liz) (Ned Sue) (Pat)
(Bob) (Don) (Jim Joe) (Liz) (Ned) (Pat Sue)
(Bob) (Don) (Jim Liz) (Joe Ned) (Pat) (Sue)
(Bob) (Don) (Jim Liz) (Joe Pat) (Ned) (Sue)
(Bob) (Don) (Jim Liz) (Joe Sue) (Ned) (Pat)
(Bob) (Don) (Jim Liz) (Joe) (Ned Pat) (Sue)
(Bob) (Don) (Jim Liz) (Joe) (Ned Sue) (Pat)
(Bob) (Don) (Jim Liz) (Joe) (Ned) (Pat Sue)
(Bob) (Don) (Jim Ned) (Joe Liz) (Pat) (Sue)
(Bob) (Don) (Jim Ned) (Joe Pat) (Liz) (Sue)
(Bob) (Don) (Jim Ned) (Joe Sue) (Liz) (Pat)
(Bob) (Don) (Jim Ned) (Joe) (Liz Pat) (Sue)
(Bob) (Don) (Jim Ned) (Joe) (Liz Sue) (Pat)
(Bob) (Don) (Jim Ned) (Joe) (Liz) (Pat Sue)
(Bob) (Don) (Jim Pat) (Joe Liz) (Ned) (Sue)
(Bob) (Don) (Jim Pat) (Joe Ned) (Liz) (Sue)
(Bob) (Don) (Jim Pat) (Joe Sue) (Liz) (Ned)
(Bob) (Don) (Jim Pat) (Joe) (Liz Sue) (Ned)
(Bob) (Don) (Jim Pat) (Joe) (Liz) (Ned Sue)
(Bob) (Don) (Jim Sue) (Joe Liz) (Ned) (Pat)
(Bob) (Don) (Jim Sue) (Joe Ned) (Liz) (Pat)
(Bob) (Don) (Jim Sue) (Joe Pat) (Liz) (Ned)
(Bob) (Don) (Jim Sue) (Joe) (Liz Pat) (Ned)
(Bob) (Don) (Jim Sue) (Joe) (Liz) (Ned Pat)
(Bob) (Don) (Jim) (Joe Liz) (Ned Pat) (Sue)
(Bob) (Don) (Jim) (Joe Liz) (Ned Sue) (Pat)
(Bob) (Don) (Jim) (Joe Liz) (Ned) (Pat Sue)
(Bob) (Don) (Jim) (Joe Ned) (Liz Pat) (Sue)
(Bob) (Don) (Jim) (Joe Ned) (Liz Sue) (Pat)
(Bob) (Don) (Jim) (Joe Ned) (Liz) (Pat Sue)
(Bob) (Don) (Jim) (Joe Pat) (Liz Sue) (Ned)
(Bob) (Don) (Jim) (Joe Pat) (Liz) (Ned Sue)
(Bob) (Don) (Jim) (Joe Sue) (Liz Pat) (Ned)
(Bob) (Don) (Jim) (Joe Sue) (Liz) (Ned Pat)
(Bob) (Don) (Jim) (Joe) (Liz Pat) (Ned Sue)
(Bob) (Don) (Jim) (Joe) (Liz Sue) (Ned Pat)

Group size template: 4 1 1 1 1
(Bob Don Jim Liz) (Joe) (Ned) (Pat) (Sue)
(Bob Don Jim Ned) (Joe) (Liz) (Pat) (Sue)
(Bob Don Jim Pat) (Joe) (Liz) (Ned) (Sue)
(Bob Don Jim Sue) (Joe) (Liz) (Ned) (Pat)
(Bob Don Liz Pat) (Jim) (Joe) (Ned) (Sue)
(Bob Don Liz Sue) (Jim) (Joe) (Ned) (Pat)
(Bob Don Ned Pat) (Jim) (Joe) (Liz) (Sue)
(Bob Don Ned Sue) (Jim) (Joe) (Liz) (Pat)
(Bob Don Pat Sue) (Jim) (Joe) (Liz) (Ned)
(Bob Jim Liz Pat) (Don) (Joe) (Ned) (Sue)
(Bob Jim Liz Sue) (Don) (Joe) (Ned) (Pat)
(Bob Jim Ned Pat) (Don) (Joe) (Liz) (Sue)
(Bob Jim Ned Sue) (Don) (Joe) (Liz) (Pat)
(Bob Jim Pat Sue) (Don) (Joe) (Liz) (Ned)
(Bob Liz Pat Sue) (Don) (Jim) (Joe) (Ned)
(Bob Ned Pat Sue) (Don) (Jim) (Joe) (Liz)
(Bob) (Don Jim Joe Liz) (Ned) (Pat) (Sue)
(Bob) (Don Jim Joe Ned) (Liz) (Pat) (Sue)
(Bob) (Don Jim Joe Pat) (Liz) (Ned) (Sue)
(Bob) (Don Jim Joe Sue) (Liz) (Ned) (Pat)
(Bob) (Don Jim Liz Pat) (Joe) (Ned) (Sue)
(Bob) (Don Jim Liz Sue) (Joe) (Ned) (Pat)
(Bob) (Don Jim Ned Pat) (Joe) (Liz) (Sue)
(Bob) (Don Jim Ned Sue) (Joe) (Liz) (Pat)
(Bob) (Don Jim Pat Sue) (Joe) (Liz) (Ned)
(Bob) (Don Joe Liz Pat) (Jim) (Ned) (Sue)
(Bob) (Don Joe Liz Sue) (Jim) (Ned) (Pat)
(Bob) (Don Joe Ned Pat) (Jim) (Liz) (Sue)
(Bob) (Don Joe Ned Sue) (Jim) (Liz) (Pat)
(Bob) (Don Joe Pat Sue) (Jim) (Liz) (Ned)
(Bob) (Don Liz Pat Sue) (Jim) (Joe) (Ned)
(Bob) (Don Ned Pat Sue) (Jim) (Joe) (Liz)
(Bob) (Don) (Jim Joe Liz Pat) (Ned) (Sue)
(Bob) (Don) (Jim Joe Liz Sue) (Ned) (Pat)
(Bob) (Don) (Jim Joe Ned Pat) (Liz) (Sue)
(Bob) (Don) (Jim Joe Ned Sue) (Liz) (Pat)
(Bob) (Don) (Jim Joe Pat Sue) (Liz) (Ned)
(Bob) (Don) (Jim Liz Pat Sue) (Joe) (Ned)
(Bob) (Don) (Jim Ned Pat Sue) (Joe) (Liz)
(Bob) (Don) (Jim) (Joe Liz Pat Sue) (Ned)
(Bob) (Don) (Jim) (Joe Ned Pat Sue) (Liz)

Group size template: 3 2 1 1 1
(Bob Don Jim) (Joe Liz) (Ned) (Pat) (Sue)
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(Bob Jim) (Don) (Joe) (Liz) (Ned Pat Sue)
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(Bob) (Don Joe Liz Pat Sue) (Jim) (Ned)
(Bob) (Don Joe Ned Pat Sue) (Jim) (Liz)
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(Bob) (Don) (Jim Joe Ned Pat Sue) (Liz)

Group size template: 2 2 2 1 1
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(Bob Don Jim Liz) (Joe Ned) (Pat) (Sue)
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Group size template: 3 3 1 1
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(Bob) (Don Ned Pat) (Jim) (Joe Liz Sue)
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(Bob Don Jim Liz Pat Sue) (Joe) (Ned)
(Bob Don Jim Ned Pat Sue) (Joe) (Liz)
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(Bob) (Don Jim Joe Ned Pat Sue) (Liz)

Group size template: 3 2 2 1
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(Bob) (Don Joe) (Jim Ned Sue) (Liz Pat)
(Bob) (Don Liz) (Jim Ned Sue) (Joe Pat)
(Bob) (Don Pat) (Jim Ned Sue) (Joe Liz)
(Bob Don) (Jim Pat Sue) (Joe Liz) (Ned)
(Bob Don) (Jim Pat Sue) (Joe Ned) (Liz)
(Bob Liz) (Don Joe) (Jim Pat Sue) (Ned)
(Bob Liz) (Don Ned) (Jim Pat Sue) (Joe)
(Bob Liz) (Don) (Jim Pat Sue) (Joe Ned)
(Bob Ned) (Don Joe) (Jim Pat Sue) (Liz)
(Bob Ned) (Don Liz) (Jim Pat Sue) (Joe)
(Bob Ned) (Don) (Jim Pat Sue) (Joe Liz)
(Bob) (Don Liz) (Jim Pat Sue) (Joe Ned)
(Bob) (Don Ned) (Jim Pat Sue) (Joe Liz)
(Bob Don) (Jim Ned) (Joe Liz Pat) (Sue)
(Bob Don) (Jim Sue) (Joe Liz Pat) (Ned)
(Bob Don) (Jim) (Joe Liz Pat) (Ned Sue)
(Bob Jim) (Don Ned) (Joe Liz Pat) (Sue)
(Bob Jim) (Don Sue) (Joe Liz Pat) (Ned)
(Bob Jim) (Don) (Joe Liz Pat) (Ned Sue)
(Bob Ned) (Don Jim) (Joe Liz Pat) (Sue)
(Bob Ned) (Don Sue) (Jim) (Joe Liz Pat)
(Bob Ned) (Don) (Jim Sue) (Joe Liz Pat)
(Bob Sue) (Don Jim) (Joe Liz Pat) (Ned)
(Bob Sue) (Don Ned) (Jim) (Joe Liz Pat)
(Bob Sue) (Don) (Jim Ned) (Joe Liz Pat)
(Bob) (Don Jim) (Joe Liz Pat) (Ned Sue)
(Bob) (Don Ned) (Jim Sue) (Joe Liz Pat)
(Bob) (Don Sue) (Jim Ned) (Joe Liz Pat)
(Bob Don) (Jim Ned) (Joe Liz Sue) (Pat)
(Bob Don) (Jim Pat) (Joe Liz Sue) (Ned)
(Bob Don) (Jim) (Joe Liz Sue) (Ned Pat)
(Bob Jim) (Don Ned) (Joe Liz Sue) (Pat)
(Bob Jim) (Don Pat) (Joe Liz Sue) (Ned)
(Bob Jim) (Don) (Joe Liz Sue) (Ned Pat)
(Bob Ned) (Don Jim) (Joe Liz Sue) (Pat)
(Bob Ned) (Don Pat) (Jim) (Joe Liz Sue)
(Bob Ned) (Don) (Jim Pat) (Joe Liz Sue)
(Bob Pat) (Don Jim) (Joe Liz Sue) (Ned)
(Bob Pat) (Don Ned) (Jim) (Joe Liz Sue)
(Bob Pat) (Don) (Jim Ned) (Joe Liz Sue)
(Bob) (Don Jim) (Joe Liz Sue) (Ned Pat)
(Bob) (Don Ned) (Jim Pat) (Joe Liz Sue)
(Bob) (Don Pat) (Jim Ned) (Joe Liz Sue)
(Bob Don) (Jim Liz) (Joe Ned Pat) (Sue)
(Bob Don) (Jim Sue) (Joe Ned Pat) (Liz)
(Bob Don) (Jim) (Joe Ned Pat) (Liz Sue)
(Bob Jim) (Don Liz) (Joe Ned Pat) (Sue)
(Bob Jim) (Don Sue) (Joe Ned Pat) (Liz)
(Bob Jim) (Don) (Joe Ned Pat) (Liz Sue)
(Bob Liz) (Don Jim) (Joe Ned Pat) (Sue)
(Bob Liz) (Don Sue) (Jim) (Joe Ned Pat)
(Bob Liz) (Don) (Jim Sue) (Joe Ned Pat)
(Bob Sue) (Don Jim) (Joe Ned Pat) (Liz)
(Bob Sue) (Don Liz) (Jim) (Joe Ned Pat)
(Bob Sue) (Don) (Jim Liz) (Joe Ned Pat)
(Bob) (Don Jim) (Joe Ned Pat) (Liz Sue)
(Bob) (Don Liz) (Jim Sue) (Joe Ned Pat)
(Bob) (Don Sue) (Jim Liz) (Joe Ned Pat)
(Bob Don) (Jim Liz) (Joe Ned Sue) (Pat)
(Bob Don) (Jim Pat) (Joe Ned Sue) (Liz)
(Bob Don) (Jim) (Joe Ned Sue) (Liz Pat)
(Bob Jim) (Don Liz) (Joe Ned Sue) (Pat)
(Bob Jim) (Don Pat) (Joe Ned Sue) (Liz)
(Bob Jim) (Don) (Joe Ned Sue) (Liz Pat)
(Bob Liz) (Don Jim) (Joe Ned Sue) (Pat)
(Bob Liz) (Don Pat) (Jim) (Joe Ned Sue)
(Bob Liz) (Don) (Jim Pat) (Joe Ned Sue)
(Bob Pat) (Don Jim) (Joe Ned Sue) (Liz)
(Bob Pat) (Don Liz) (Jim) (Joe Ned Sue)
(Bob Pat) (Don) (Jim Liz) (Joe Ned Sue)
(Bob) (Don Jim) (Joe Ned Sue) (Liz Pat)
(Bob) (Don Liz) (Jim Pat) (Joe Ned Sue)
(Bob) (Don Pat) (Jim Liz) (Joe Ned Sue)
(Bob Don) (Jim Liz) (Joe Pat Sue) (Ned)
(Bob Don) (Jim Ned) (Joe Pat Sue) (Liz)
(Bob Jim) (Don Liz) (Joe Pat Sue) (Ned)
(Bob Jim) (Don Ned) (Joe Pat Sue) (Liz)
(Bob Liz) (Don Jim) (Joe Pat Sue) (Ned)
(Bob Liz) (Don Ned) (Jim) (Joe Pat Sue)
(Bob Liz) (Don) (Jim Ned) (Joe Pat Sue)
(Bob Ned) (Don Jim) (Joe Pat Sue) (Liz)
(Bob Ned) (Don Liz) (Jim) (Joe Pat Sue)
(Bob Ned) (Don) (Jim Liz) (Joe Pat Sue)
(Bob) (Don Liz) (Jim Ned) (Joe Pat Sue)
(Bob) (Don Ned) (Jim Liz) (Joe Pat Sue)
(Bob Don) (Jim Joe) (Liz Pat Sue) (Ned)
(Bob Don) (Jim Ned) (Joe) (Liz Pat Sue)
(Bob Don) (Jim) (Joe Ned) (Liz Pat Sue)
(Bob Jim) (Don Joe) (Liz Pat Sue) (Ned)
(Bob Jim) (Don Ned) (Joe) (Liz Pat Sue)
(Bob Jim) (Don) (Joe Ned) (Liz Pat Sue)
(Bob Ned) (Don Jim) (Joe) (Liz Pat Sue)
(Bob Ned) (Don Joe) (Jim) (Liz Pat Sue)
(Bob Ned) (Don) (Jim Joe) (Liz Pat Sue)
(Bob) (Don Jim) (Joe Ned) (Liz Pat Sue)
(Bob) (Don Joe) (Jim Ned) (Liz Pat Sue)
(Bob) (Don Ned) (Jim Joe) (Liz Pat Sue)
(Bob Don) (Jim Joe) (Liz) (Ned Pat Sue)
(Bob Don) (Jim Liz) (Joe) (Ned Pat Sue)
(Bob Don) (Jim) (Joe Liz) (Ned Pat Sue)
(Bob Jim) (Don Joe) (Liz) (Ned Pat Sue)
(Bob Jim) (Don Liz) (Joe) (Ned Pat Sue)
(Bob Jim) (Don) (Joe Liz) (Ned Pat Sue)
(Bob Liz) (Don Jim) (Joe) (Ned Pat Sue)
(Bob Liz) (Don Joe) (Jim) (Ned Pat Sue)
(Bob Liz) (Don) (Jim Joe) (Ned Pat Sue)
(Bob) (Don Jim) (Joe Liz) (Ned Pat Sue)
(Bob) (Don Joe) (Jim Liz) (Ned Pat Sue)
(Bob) (Don Liz) (Jim Joe) (Ned Pat Sue)

Group size template: 5 2 1
(Bob Don Jim Liz Pat) (Joe Ned) (Sue)
(Bob Don Jim Liz Pat) (Joe Sue) (Ned)
(Bob Don Jim Liz Pat) (Joe) (Ned Sue)
(Bob Don Jim Liz Sue) (Joe Ned) (Pat)
(Bob Don Jim Liz Sue) (Joe Pat) (Ned)
(Bob Don Jim Liz Sue) (Joe) (Ned Pat)
(Bob Don Jim Ned Pat) (Joe Liz) (Sue)
(Bob Don Jim Ned Pat) (Joe Sue) (Liz)
(Bob Don Jim Ned Pat) (Joe) (Liz Sue)
(Bob Don Jim Ned Sue) (Joe Liz) (Pat)
(Bob Don Jim Ned Sue) (Joe Pat) (Liz)
(Bob Don Jim Ned Sue) (Joe) (Liz Pat)
(Bob Don Jim Pat Sue) (Joe Liz) (Ned)
(Bob Don Jim Pat Sue) (Joe Ned) (Liz)
(Bob Don Liz Pat Sue) (Jim Joe) (Ned)
(Bob Don Liz Pat Sue) (Jim Ned) (Joe)
(Bob Don Liz Pat Sue) (Jim) (Joe Ned)
(Bob Don Ned Pat Sue) (Jim Joe) (Liz)
(Bob Don Ned Pat Sue) (Jim Liz) (Joe)
(Bob Don Ned Pat Sue) (Jim) (Joe Liz)
(Bob Jim Liz Pat Sue) (Don Joe) (Ned)
(Bob Jim Liz Pat Sue) (Don Ned) (Joe)
(Bob Jim Liz Pat Sue) (Don) (Joe Ned)
(Bob Jim Ned Pat Sue) (Don Joe) (Liz)
(Bob Jim Ned Pat Sue) (Don Liz) (Joe)
(Bob Jim Ned Pat Sue) (Don) (Joe Liz)
(Bob Ned) (Don Jim Joe Liz Pat) (Sue)
(Bob Sue) (Don Jim Joe Liz Pat) (Ned)
(Bob) (Don Jim Joe Liz Pat) (Ned Sue)
(Bob Ned) (Don Jim Joe Liz Sue) (Pat)
(Bob Pat) (Don Jim Joe Liz Sue) (Ned)
(Bob) (Don Jim Joe Liz Sue) (Ned Pat)
(Bob Liz) (Don Jim Joe Ned Pat) (Sue)
(Bob Sue) (Don Jim Joe Ned Pat) (Liz)
(Bob) (Don Jim Joe Ned Pat) (Liz Sue)
(Bob Liz) (Don Jim Joe Ned Sue) (Pat)
(Bob Pat) (Don Jim Joe Ned Sue) (Liz)
(Bob) (Don Jim Joe Ned Sue) (Liz Pat)
(Bob Liz) (Don Jim Joe Pat Sue) (Ned)
(Bob Ned) (Don Jim Joe Pat Sue) (Liz)
(Bob Ned) (Don Jim Liz Pat Sue) (Joe)
(Bob) (Don Jim Liz Pat Sue) (Joe Ned)
(Bob Liz) (Don Jim Ned Pat Sue) (Joe)
(Bob) (Don Jim Ned Pat Sue) (Joe Liz)
(Bob Jim) (Don Joe Liz Pat Sue) (Ned)
(Bob Ned) (Don Joe Liz Pat Sue) (Jim)
(Bob) (Don Joe Liz Pat Sue) (Jim Ned)
(Bob Jim) (Don Joe Ned Pat Sue) (Liz)
(Bob Liz) (Don Joe Ned Pat Sue) (Jim)
(Bob) (Don Joe Ned Pat Sue) (Jim Liz)
(Bob Don) (Jim Joe Liz Pat Sue) (Ned)
(Bob Ned) (Don) (Jim Joe Liz Pat Sue)
(Bob) (Don Ned) (Jim Joe Liz Pat Sue)
(Bob Don) (Jim Joe Ned Pat Sue) (Liz)
(Bob Liz) (Don) (Jim Joe Ned Pat Sue)
(Bob) (Don Liz) (Jim Joe Ned Pat Sue)

Group size template: 4 3 1
(Bob Don Jim Liz) (Joe Ned Pat) (Sue)
(Bob Don Jim Liz) (Joe Ned Sue) (Pat)
(Bob Don Jim Liz) (Joe Pat Sue) (Ned)
(Bob Don Jim Liz) (Joe) (Ned Pat Sue)
(Bob Don Jim Ned) (Joe Liz Pat) (Sue)
(Bob Don Jim Ned) (Joe Liz Sue) (Pat)
(Bob Don Jim Ned) (Joe Pat Sue) (Liz)
(Bob Don Jim Ned) (Joe) (Liz Pat Sue)
(Bob Don Jim Pat) (Joe Liz Sue) (Ned)
(Bob Don Jim Pat) (Joe Ned Sue) (Liz)
(Bob Don Jim Sue) (Joe Liz Pat) (Ned)
(Bob Don Jim Sue) (Joe Ned Pat) (Liz)
(Bob Don Liz Pat) (Jim Joe Ned) (Sue)
(Bob Don Liz Pat) (Jim Joe Sue) (Ned)
(Bob Don Liz Pat) (Jim Ned Sue) (Joe)
(Bob Don Liz Pat) (Jim) (Joe Ned Sue)
(Bob Don Liz Sue) (Jim Joe Ned) (Pat)
(Bob Don Liz Sue) (Jim Joe Pat) (Ned)
(Bob Don Liz Sue) (Jim Ned Pat) (Joe)
(Bob Don Liz Sue) (Jim) (Joe Ned Pat)
(Bob Don Ned Pat) (Jim Joe Liz) (Sue)
(Bob Don Ned Pat) (Jim Joe Sue) (Liz)
(Bob Don Ned Pat) (Jim Liz Sue) (Joe)
(Bob Don Ned Pat) (Jim) (Joe Liz Sue)
(Bob Don Ned Sue) (Jim Joe Liz) (Pat)
(Bob Don Ned Sue) (Jim Joe Pat) (Liz)
(Bob Don Ned Sue) (Jim Liz Pat) (Joe)
(Bob Don Ned Sue) (Jim) (Joe Liz Pat)
(Bob Don Pat Sue) (Jim Joe Liz) (Ned)
(Bob Don Pat Sue) (Jim Joe Ned) (Liz)
(Bob Jim Liz Pat) (Don Joe Ned) (Sue)
(Bob Jim Liz Pat) (Don Joe Sue) (Ned)
(Bob Jim Liz Pat) (Don Ned Sue) (Joe)
(Bob Jim Liz Pat) (Don) (Joe Ned Sue)
(Bob Jim Liz Sue) (Don Joe Ned) (Pat)
(Bob Jim Liz Sue) (Don Joe Pat) (Ned)
(Bob Jim Liz Sue) (Don Ned Pat) (Joe)
(Bob Jim Liz Sue) (Don) (Joe Ned Pat)
(Bob Jim Ned Pat) (Don Joe Liz) (Sue)
(Bob Jim Ned Pat) (Don Joe Sue) (Liz)
(Bob Jim Ned Pat) (Don Liz Sue) (Joe)
(Bob Jim Ned Pat) (Don) (Joe Liz Sue)
(Bob Jim Ned Sue) (Don Joe Liz) (Pat)
(Bob Jim Ned Sue) (Don Joe Pat) (Liz)
(Bob Jim Ned Sue) (Don Liz Pat) (Joe)
(Bob Jim Ned Sue) (Don) (Joe Liz Pat)
(Bob Jim Pat Sue) (Don Joe Liz) (Ned)
(Bob Jim Pat Sue) (Don Joe Ned) (Liz)
(Bob Liz Pat Sue) (Don Jim Joe) (Ned)
(Bob Liz Pat Sue) (Don Jim Ned) (Joe)
(Bob Liz Pat Sue) (Don Joe Ned) (Jim)
(Bob Liz Pat Sue) (Don) (Jim Joe Ned)
(Bob Ned Pat Sue) (Don Jim Joe) (Liz)
(Bob Ned Pat Sue) (Don Jim Liz) (Joe)
(Bob Ned Pat Sue) (Don Joe Liz) (Jim)
(Bob Ned Pat Sue) (Don) (Jim Joe Liz)
(Bob Ned Pat) (Don Jim Joe Liz) (Sue)
(Bob Ned Sue) (Don Jim Joe Liz) (Pat)
(Bob Pat Sue) (Don Jim Joe Liz) (Ned)
(Bob) (Don Jim Joe Liz) (Ned Pat Sue)
(Bob Liz Pat) (Don Jim Joe Ned) (Sue)
(Bob Liz Sue) (Don Jim Joe Ned) (Pat)
(Bob Pat Sue) (Don Jim Joe Ned) (Liz)
(Bob) (Don Jim Joe Ned) (Liz Pat Sue)
(Bob Liz Sue) (Don Jim Joe Pat) (Ned)
(Bob Ned Sue) (Don Jim Joe Pat) (Liz)
(Bob Liz Pat) (Don Jim Joe Sue) (Ned)
(Bob Ned Pat) (Don Jim Joe Sue) (Liz)
(Bob Ned Sue) (Don Jim Liz Pat) (Joe)
(Bob) (Don Jim Liz Pat) (Joe Ned Sue)
(Bob Ned Pat) (Don Jim Liz Sue) (Joe)
(Bob) (Don Jim Liz Sue) (Joe Ned Pat)
(Bob Liz Sue) (Don Jim Ned Pat) (Joe)
(Bob) (Don Jim Ned Pat) (Joe Liz Sue)
(Bob Liz Pat) (Don Jim Ned Sue) (Joe)
(Bob) (Don Jim Ned Sue) (Joe Liz Pat)
(Bob Jim Ned) (Don Joe Liz Pat) (Sue)
(Bob Jim Sue) (Don Joe Liz Pat) (Ned)
(Bob Ned Sue) (Don Joe Liz Pat) (Jim)
(Bob) (Don Joe Liz Pat) (Jim Ned Sue)
(Bob Jim Ned) (Don Joe Liz Sue) (Pat)
(Bob Jim Pat) (Don Joe Liz Sue) (Ned)
(Bob Ned Pat) (Don Joe Liz Sue) (Jim)
(Bob) (Don Joe Liz Sue) (Jim Ned Pat)
(Bob Jim Liz) (Don Joe Ned Pat) (Sue)
(Bob Jim Sue) (Don Joe Ned Pat) (Liz)
(Bob Liz Sue) (Don Joe Ned Pat) (Jim)
(Bob) (Don Joe Ned Pat) (Jim Liz Sue)
(Bob Jim Liz) (Don Joe Ned Sue) (Pat)
(Bob Jim Pat) (Don Joe Ned Sue) (Liz)
(Bob Liz Pat) (Don Joe Ned Sue) (Jim)
(Bob) (Don Joe Ned Sue) (Jim Liz Pat)
(Bob Jim Liz) (Don Joe Pat Sue) (Ned)
(Bob Jim Ned) (Don Joe Pat Sue) (Liz)
(Bob Jim Ned) (Don Liz Pat Sue) (Joe)
(Bob) (Don Liz Pat Sue) (Jim Joe Ned)
(Bob Jim Liz) (Don Ned Pat Sue) (Joe)
(Bob) (Don Ned Pat Sue) (Jim Joe Liz)
(Bob Don Ned) (Jim Joe Liz Pat) (Sue)
(Bob Don Sue) (Jim Joe Liz Pat) (Ned)
(Bob Ned Sue) (Don) (Jim Joe Liz Pat)
(Bob) (Don Ned Sue) (Jim Joe Liz Pat)
(Bob Don Ned) (Jim Joe Liz Sue) (Pat)
(Bob Don Pat) (Jim Joe Liz Sue) (Ned)
(Bob Ned Pat) (Don) (Jim Joe Liz Sue)
(Bob) (Don Ned Pat) (Jim Joe Liz Sue)
(Bob Don Liz) (Jim Joe Ned Pat) (Sue)
(Bob Don Sue) (Jim Joe Ned Pat) (Liz)
(Bob Liz Sue) (Don) (Jim Joe Ned Pat)
(Bob) (Don Liz Sue) (Jim Joe Ned Pat)
(Bob Don Liz) (Jim Joe Ned Sue) (Pat)
(Bob Don Pat) (Jim Joe Ned Sue) (Liz)
(Bob Liz Pat) (Don) (Jim Joe Ned Sue)
(Bob) (Don Liz Pat) (Jim Joe Ned Sue)
(Bob Don Liz) (Jim Joe Pat Sue) (Ned)
(Bob Don Ned) (Jim Joe Pat Sue) (Liz)
(Bob Don Ned) (Jim Liz Pat Sue) (Joe)
(Bob) (Don Joe Ned) (Jim Liz Pat Sue)
(Bob Don Liz) (Jim Ned Pat Sue) (Joe)
(Bob) (Don Joe Liz) (Jim Ned Pat Sue)
(Bob Don Jim) (Joe Liz Pat Sue) (Ned)
(Bob Don Ned) (Jim) (Joe Liz Pat Sue)
(Bob Jim Ned) (Don) (Joe Liz Pat Sue)
(Bob) (Don Jim Ned) (Joe Liz Pat Sue)
(Bob Don Jim) (Joe Ned Pat Sue) (Liz)
(Bob Don Liz) (Jim) (Joe Ned Pat Sue)
(Bob Jim Liz) (Don) (Joe Ned Pat Sue)
(Bob) (Don Jim Liz) (Joe Ned Pat Sue)

Group size template: 2 2 2 2
(Bob Don) (Jim Joe) (Liz Pat) (Ned Sue)
(Bob Don) (Jim Joe) (Liz Sue) (Ned Pat)
(Bob Don) (Jim Liz) (Joe Ned) (Pat Sue)
(Bob Don) (Jim Liz) (Joe Pat) (Ned Sue)
(Bob Don) (Jim Liz) (Joe Sue) (Ned Pat)
(Bob Don) (Jim Ned) (Joe Liz) (Pat Sue)
(Bob Don) (Jim Ned) (Joe Pat) (Liz Sue)
(Bob Don) (Jim Ned) (Joe Sue) (Liz Pat)
(Bob Don) (Jim Pat) (Joe Liz) (Ned Sue)
(Bob Don) (Jim Pat) (Joe Ned) (Liz Sue)
(Bob Don) (Jim Sue) (Joe Liz) (Ned Pat)
(Bob Don) (Jim Sue) (Joe Ned) (Liz Pat)
(Bob Jim) (Don Joe) (Liz Pat) (Ned Sue)
(Bob Jim) (Don Joe) (Liz Sue) (Ned Pat)
(Bob Jim) (Don Liz) (Joe Ned) (Pat Sue)
(Bob Jim) (Don Liz) (Joe Pat) (Ned Sue)
(Bob Jim) (Don Liz) (Joe Sue) (Ned Pat)
(Bob Jim) (Don Ned) (Joe Liz) (Pat Sue)
(Bob Jim) (Don Ned) (Joe Pat) (Liz Sue)
(Bob Jim) (Don Ned) (Joe Sue) (Liz Pat)
(Bob Jim) (Don Pat) (Joe Liz) (Ned Sue)
(Bob Jim) (Don Pat) (Joe Ned) (Liz Sue)
(Bob Jim) (Don Sue) (Joe Liz) (Ned Pat)
(Bob Jim) (Don Sue) (Joe Ned) (Liz Pat)
(Bob Liz) (Don Jim) (Joe Ned) (Pat Sue)
(Bob Liz) (Don Jim) (Joe Pat) (Ned Sue)
(Bob Liz) (Don Jim) (Joe Sue) (Ned Pat)
(Bob Liz) (Don Joe) (Jim Ned) (Pat Sue)
(Bob Liz) (Don Joe) (Jim Pat) (Ned Sue)
(Bob Liz) (Don Joe) (Jim Sue) (Ned Pat)
(Bob Liz) (Don Ned) (Jim Joe) (Pat Sue)
(Bob Liz) (Don Ned) (Jim Pat) (Joe Sue)
(Bob Liz) (Don Ned) (Jim Sue) (Joe Pat)
(Bob Liz) (Don Pat) (Jim Joe) (Ned Sue)
(Bob Liz) (Don Pat) (Jim Ned) (Joe Sue)
(Bob Liz) (Don Pat) (Jim Sue) (Joe Ned)
(Bob Liz) (Don Sue) (Jim Joe) (Ned Pat)
(Bob Liz) (Don Sue) (Jim Ned) (Joe Pat)
(Bob Liz) (Don Sue) (Jim Pat) (Joe Ned)
(Bob Ned) (Don Jim) (Joe Liz) (Pat Sue)
(Bob Ned) (Don Jim) (Joe Pat) (Liz Sue)
(Bob Ned) (Don Jim) (Joe Sue) (Liz Pat)
(Bob Ned) (Don Joe) (Jim Liz) (Pat Sue)
(Bob Ned) (Don Joe) (Jim Pat) (Liz Sue)
(Bob Ned) (Don Joe) (Jim Sue) (Liz Pat)
(Bob Ned) (Don Liz) (Jim Joe) (Pat Sue)
(Bob Ned) (Don Liz) (Jim Pat) (Joe Sue)
(Bob Ned) (Don Liz) (Jim Sue) (Joe Pat)
(Bob Ned) (Don Pat) (Jim Joe) (Liz Sue)
(Bob Ned) (Don Pat) (Jim Liz) (Joe Sue)
(Bob Ned) (Don Pat) (Jim Sue) (Joe Liz)
(Bob Ned) (Don Sue) (Jim Joe) (Liz Pat)
(Bob Ned) (Don Sue) (Jim Liz) (Joe Pat)
(Bob Ned) (Don Sue) (Jim Pat) (Joe Liz)
(Bob Pat) (Don Jim) (Joe Liz) (Ned Sue)
(Bob Pat) (Don Jim) (Joe Ned) (Liz Sue)
(Bob Pat) (Don Joe) (Jim Liz) (Ned Sue)
(Bob Pat) (Don Joe) (Jim Ned) (Liz Sue)
(Bob Pat) (Don Liz) (Jim Joe) (Ned Sue)
(Bob Pat) (Don Liz) (Jim Ned) (Joe Sue)
(Bob Pat) (Don Liz) (Jim Sue) (Joe Ned)
(Bob Pat) (Don Ned) (Jim Joe) (Liz Sue)
(Bob Pat) (Don Ned) (Jim Liz) (Joe Sue)
(Bob Pat) (Don Ned) (Jim Sue) (Joe Liz)
(Bob Pat) (Don Sue) (Jim Liz) (Joe Ned)
(Bob Pat) (Don Sue) (Jim Ned) (Joe Liz)
(Bob Sue) (Don Jim) (Joe Liz) (Ned Pat)
(Bob Sue) (Don Jim) (Joe Ned) (Liz Pat)
(Bob Sue) (Don Joe) (Jim Liz) (Ned Pat)
(Bob Sue) (Don Joe) (Jim Ned) (Liz Pat)
(Bob Sue) (Don Liz) (Jim Joe) (Ned Pat)
(Bob Sue) (Don Liz) (Jim Ned) (Joe Pat)
(Bob Sue) (Don Liz) (Jim Pat) (Joe Ned)
(Bob Sue) (Don Ned) (Jim Joe) (Liz Pat)
(Bob Sue) (Don Ned) (Jim Liz) (Joe Pat)
(Bob Sue) (Don Ned) (Jim Pat) (Joe Liz)
(Bob Sue) (Don Pat) (Jim Liz) (Joe Ned)
(Bob Sue) (Don Pat) (Jim Ned) (Joe Liz)

Group size template: 4 2 2
(Bob Don Jim Liz) (Joe Ned) (Pat Sue)
(Bob Don Jim Liz) (Joe Pat) (Ned Sue)
(Bob Don Jim Liz) (Joe Sue) (Ned Pat)
(Bob Don Jim Ned) (Joe Liz) (Pat Sue)
(Bob Don Jim Ned) (Joe Pat) (Liz Sue)
(Bob Don Jim Ned) (Joe Sue) (Liz Pat)
(Bob Don Jim Pat) (Joe Liz) (Ned Sue)
(Bob Don Jim Pat) (Joe Ned) (Liz Sue)
(Bob Don Jim Sue) (Joe Liz) (Ned Pat)
(Bob Don Jim Sue) (Joe Ned) (Liz Pat)
(Bob Don Liz Pat) (Jim Joe) (Ned Sue)
(Bob Don Liz Pat) (Jim Ned) (Joe Sue)
(Bob Don Liz Pat) (Jim Sue) (Joe Ned)
(Bob Don Liz Sue) (Jim Joe) (Ned Pat)
(Bob Don Liz Sue) (Jim Ned) (Joe Pat)
(Bob Don Liz Sue) (Jim Pat) (Joe Ned)
(Bob Don Ned Pat) (Jim Joe) (Liz Sue)
(Bob Don Ned Pat) (Jim Liz) (Joe Sue)
(Bob Don Ned Pat) (Jim Sue) (Joe Liz)
(Bob Don Ned Sue) (Jim Joe) (Liz Pat)
(Bob Don Ned Sue) (Jim Liz) (Joe Pat)
(Bob Don Ned Sue) (Jim Pat) (Joe Liz)
(Bob Don Pat Sue) (Jim Liz) (Joe Ned)
(Bob Don Pat Sue) (Jim Ned) (Joe Liz)
(Bob Jim Liz Pat) (Don Joe) (Ned Sue)
(Bob Jim Liz Pat) (Don Ned) (Joe Sue)
(Bob Jim Liz Pat) (Don Sue) (Joe Ned)
(Bob Jim Liz Sue) (Don Joe) (Ned Pat)
(Bob Jim Liz Sue) (Don Ned) (Joe Pat)
(Bob Jim Liz Sue) (Don Pat) (Joe Ned)
(Bob Jim Ned Pat) (Don Joe) (Liz Sue)
(Bob Jim Ned Pat) (Don Liz) (Joe Sue)
(Bob Jim Ned Pat) (Don Sue) (Joe Liz)
(Bob Jim Ned Sue) (Don Joe) (Liz Pat)
(Bob Jim Ned Sue) (Don Liz) (Joe Pat)
(Bob Jim Ned Sue) (Don Pat) (Joe Liz)
(Bob Jim Pat Sue) (Don Liz) (Joe Ned)
(Bob Jim Pat Sue) (Don Ned) (Joe Liz)
(Bob Liz Pat Sue) (Don Jim) (Joe Ned)
(Bob Liz Pat Sue) (Don Joe) (Jim Ned)
(Bob Liz Pat Sue) (Don Ned) (Jim Joe)
(Bob Ned Pat Sue) (Don Jim) (Joe Liz)
(Bob Ned Pat Sue) (Don Joe) (Jim Liz)
(Bob Ned Pat Sue) (Don Liz) (Jim Joe)
(Bob Ned) (Don Jim Joe Liz) (Pat Sue)
(Bob Pat) (Don Jim Joe Liz) (Ned Sue)
(Bob Sue) (Don Jim Joe Liz) (Ned Pat)
(Bob Liz) (Don Jim Joe Ned) (Pat Sue)
(Bob Pat) (Don Jim Joe Ned) (Liz Sue)
(Bob Sue) (Don Jim Joe Ned) (Liz Pat)
(Bob Liz) (Don Jim Joe Pat) (Ned Sue)
(Bob Ned) (Don Jim Joe Pat) (Liz Sue)
(Bob Liz) (Don Jim Joe Sue) (Ned Pat)
(Bob Ned) (Don Jim Joe Sue) (Liz Pat)
(Bob Ned) (Don Jim Liz Pat) (Joe Sue)
(Bob Sue) (Don Jim Liz Pat) (Joe Ned)
(Bob Ned) (Don Jim Liz Sue) (Joe Pat)
(Bob Pat) (Don Jim Liz Sue) (Joe Ned)
(Bob Liz) (Don Jim Ned Pat) (Joe Sue)
(Bob Sue) (Don Jim Ned Pat) (Joe Liz)
(Bob Liz) (Don Jim Ned Sue) (Joe Pat)
(Bob Pat) (Don Jim Ned Sue) (Joe Liz)
(Bob Liz) (Don Jim Pat Sue) (Joe Ned)
(Bob Ned) (Don Jim Pat Sue) (Joe Liz)
(Bob Jim) (Don Joe Liz Pat) (Ned Sue)
(Bob Ned) (Don Joe Liz Pat) (Jim Sue)
(Bob Sue) (Don Joe Liz Pat) (Jim Ned)
(Bob Jim) (Don Joe Liz Sue) (Ned Pat)
(Bob Ned) (Don Joe Liz Sue) (Jim Pat)
(Bob Pat) (Don Joe Liz Sue) (Jim Ned)
(Bob Jim) (Don Joe Ned Pat) (Liz Sue)
(Bob Liz) (Don Joe Ned Pat) (Jim Sue)
(Bob Sue) (Don Joe Ned Pat) (Jim Liz)
(Bob Jim) (Don Joe Ned Sue) (Liz Pat)
(Bob Liz) (Don Joe Ned Sue) (Jim Pat)
(Bob Pat) (Don Joe Ned Sue) (Jim Liz)
(Bob Liz) (Don Joe Pat Sue) (Jim Ned)
(Bob Ned) (Don Joe Pat Sue) (Jim Liz)
(Bob Jim) (Don Liz Pat Sue) (Joe Ned)
(Bob Ned) (Don Liz Pat Sue) (Jim Joe)
(Bob Jim) (Don Ned Pat Sue) (Joe Liz)
(Bob Liz) (Don Ned Pat Sue) (Jim Joe)
(Bob Don) (Jim Joe Liz Pat) (Ned Sue)
(Bob Ned) (Don Sue) (Jim Joe Liz Pat)
(Bob Sue) (Don Ned) (Jim Joe Liz Pat)
(Bob Don) (Jim Joe Liz Sue) (Ned Pat)
(Bob Ned) (Don Pat) (Jim Joe Liz Sue)
(Bob Pat) (Don Ned) (Jim Joe Liz Sue)
(Bob Don) (Jim Joe Ned Pat) (Liz Sue)
(Bob Liz) (Don Sue) (Jim Joe Ned Pat)
(Bob Sue) (Don Liz) (Jim Joe Ned Pat)
(Bob Don) (Jim Joe Ned Sue) (Liz Pat)
(Bob Liz) (Don Pat) (Jim Joe Ned Sue)
(Bob Pat) (Don Liz) (Jim Joe Ned Sue)
(Bob Liz) (Don Ned) (Jim Joe Pat Sue)
(Bob Ned) (Don Liz) (Jim Joe Pat Sue)
(Bob Don) (Jim Liz Pat Sue) (Joe Ned)
(Bob Ned) (Don Joe) (Jim Liz Pat Sue)
(Bob Don) (Jim Ned Pat Sue) (Joe Liz)
(Bob Liz) (Don Joe) (Jim Ned Pat Sue)
(Bob Don) (Jim Ned) (Joe Liz Pat Sue)
(Bob Jim) (Don Ned) (Joe Liz Pat Sue)
(Bob Ned) (Don Jim) (Joe Liz Pat Sue)
(Bob Don) (Jim Liz) (Joe Ned Pat Sue)
(Bob Jim) (Don Liz) (Joe Ned Pat Sue)
(Bob Liz) (Don Jim) (Joe Ned Pat Sue)

Group size template: 3 3 2
(Bob Don Jim) (Joe Liz Pat) (Ned Sue)
(Bob Don Jim) (Joe Liz Sue) (Ned Pat)
(Bob Don Jim) (Joe Ned Pat) (Liz Sue)
(Bob Don Jim) (Joe Ned Sue) (Liz Pat)
(Bob Don Jim) (Joe Ned) (Liz Pat Sue)
(Bob Don Jim) (Joe Liz) (Ned Pat Sue)
(Bob Don Liz) (Jim Joe Ned) (Pat Sue)
(Bob Don Liz) (Jim Joe Pat) (Ned Sue)
(Bob Don Liz) (Jim Joe Sue) (Ned Pat)
(Bob Don Liz) (Jim Ned Pat) (Joe Sue)
(Bob Don Liz) (Jim Ned Sue) (Joe Pat)
(Bob Don Liz) (Jim Pat Sue) (Joe Ned)
(Bob Don Liz) (Jim Sue) (Joe Ned Pat)
(Bob Don Liz) (Jim Pat) (Joe Ned Sue)
(Bob Don Liz) (Jim Ned) (Joe Pat Sue)
(Bob Don Liz) (Jim Joe) (Ned Pat Sue)
(Bob Don Ned) (Jim Joe Liz) (Pat Sue)
(Bob Don Ned) (Jim Joe Pat) (Liz Sue)
(Bob Don Ned) (Jim Joe Sue) (Liz Pat)
(Bob Don Ned) (Jim Liz Pat) (Joe Sue)
(Bob Don Ned) (Jim Liz Sue) (Joe Pat)
(Bob Don Ned) (Jim Pat Sue) (Joe Liz)
(Bob Don Ned) (Jim Sue) (Joe Liz Pat)
(Bob Don Ned) (Jim Pat) (Joe Liz Sue)
(Bob Don Ned) (Jim Liz) (Joe Pat Sue)
(Bob Don Ned) (Jim Joe) (Liz Pat Sue)
(Bob Don Pat) (Jim Joe Liz) (Ned Sue)
(Bob Don Pat) (Jim Joe Ned) (Liz Sue)
(Bob Don Pat) (Jim Liz Sue) (Joe Ned)
(Bob Don Pat) (Jim Ned Sue) (Joe Liz)
(Bob Don Pat) (Jim Ned) (Joe Liz Sue)
(Bob Don Pat) (Jim Liz) (Joe Ned Sue)
(Bob Don Sue) (Jim Joe Liz) (Ned Pat)
(Bob Don Sue) (Jim Joe Ned) (Liz Pat)
(Bob Don Sue) (Jim Liz Pat) (Joe Ned)
(Bob Don Sue) (Jim Ned Pat) (Joe Liz)
(Bob Don Sue) (Jim Ned) (Joe Liz Pat)
(Bob Don Sue) (Jim Liz) (Joe Ned Pat)
(Bob Jim Liz) (Don Joe Ned) (Pat Sue)
(Bob Jim Liz) (Don Joe Pat) (Ned Sue)
(Bob Jim Liz) (Don Joe Sue) (Ned Pat)
(Bob Jim Liz) (Don Ned Pat) (Joe Sue)
(Bob Jim Liz) (Don Ned Sue) (Joe Pat)
(Bob Jim Liz) (Don Pat Sue) (Joe Ned)
(Bob Jim Liz) (Don Sue) (Joe Ned Pat)
(Bob Jim Liz) (Don Pat) (Joe Ned Sue)
(Bob Jim Liz) (Don Ned) (Joe Pat Sue)
(Bob Jim Liz) (Don Joe) (Ned Pat Sue)
(Bob Jim Ned) (Don Joe Liz) (Pat Sue)
(Bob Jim Ned) (Don Joe Pat) (Liz Sue)
(Bob Jim Ned) (Don Joe Sue) (Liz Pat)
(Bob Jim Ned) (Don Liz Pat) (Joe Sue)
(Bob Jim Ned) (Don Liz Sue) (Joe Pat)
(Bob Jim Ned) (Don Pat Sue) (Joe Liz)
(Bob Jim Ned) (Don Sue) (Joe Liz Pat)
(Bob Jim Ned) (Don Pat) (Joe Liz Sue)
(Bob Jim Ned) (Don Liz) (Joe Pat Sue)
(Bob Jim Ned) (Don Joe) (Liz Pat Sue)
(Bob Jim Pat) (Don Joe Liz) (Ned Sue)
(Bob Jim Pat) (Don Joe Ned) (Liz Sue)
(Bob Jim Pat) (Don Liz Sue) (Joe Ned)
(Bob Jim Pat) (Don Ned Sue) (Joe Liz)
(Bob Jim Pat) (Don Ned) (Joe Liz Sue)
(Bob Jim Pat) (Don Liz) (Joe Ned Sue)
(Bob Jim Sue) (Don Joe Liz) (Ned Pat)
(Bob Jim Sue) (Don Joe Ned) (Liz Pat)
(Bob Jim Sue) (Don Liz Pat) (Joe Ned)
(Bob Jim Sue) (Don Ned Pat) (Joe Liz)
(Bob Jim Sue) (Don Ned) (Joe Liz Pat)
(Bob Jim Sue) (Don Liz) (Joe Ned Pat)
(Bob Liz Pat) (Don Jim Joe) (Ned Sue)
(Bob Liz Pat) (Don Jim Ned) (Joe Sue)
(Bob Liz Pat) (Don Jim Sue) (Joe Ned)
(Bob Liz Pat) (Don Joe Ned) (Jim Sue)
(Bob Liz Pat) (Don Joe Sue) (Jim Ned)
(Bob Liz Pat) (Don Ned Sue) (Jim Joe)
(Bob Liz Pat) (Don Sue) (Jim Joe Ned)
(Bob Liz Pat) (Don Ned) (Jim Joe Sue)
(Bob Liz Pat) (Don Joe) (Jim Ned Sue)
(Bob Liz Pat) (Don Jim) (Joe Ned Sue)
(Bob Liz Sue) (Don Jim Joe) (Ned Pat)
(Bob Liz Sue) (Don Jim Ned) (Joe Pat)
(Bob Liz Sue) (Don Jim Pat) (Joe Ned)
(Bob Liz Sue) (Don Joe Ned) (Jim Pat)
(Bob Liz Sue) (Don Joe Pat) (Jim Ned)
(Bob Liz Sue) (Don Ned Pat) (Jim Joe)
(Bob Liz Sue) (Don Pat) (Jim Joe Ned)
(Bob Liz Sue) (Don Ned) (Jim Joe Pat)
(Bob Liz Sue) (Don Joe) (Jim Ned Pat)
(Bob Liz Sue) (Don Jim) (Joe Ned Pat)
(Bob Ned Pat) (Don Jim Joe) (Liz Sue)
(Bob Ned Pat) (Don Jim Liz) (Joe Sue)
(Bob Ned Pat) (Don Jim Sue) (Joe Liz)
(Bob Ned Pat) (Don Joe Liz) (Jim Sue)
(Bob Ned Pat) (Don Joe Sue) (Jim Liz)
(Bob Ned Pat) (Don Liz Sue) (Jim Joe)
(Bob Ned Pat) (Don Sue) (Jim Joe Liz)
(Bob Ned Pat) (Don Liz) (Jim Joe Sue)
(Bob Ned Pat) (Don Joe) (Jim Liz Sue)
(Bob Ned Pat) (Don Jim) (Joe Liz Sue)
(Bob Ned Sue) (Don Jim Joe) (Liz Pat)
(Bob Ned Sue) (Don Jim Liz) (Joe Pat)
(Bob Ned Sue) (Don Jim Pat) (Joe Liz)
(Bob Ned Sue) (Don Joe Liz) (Jim Pat)
(Bob Ned Sue) (Don Joe Pat) (Jim Liz)
(Bob Ned Sue) (Don Liz Pat) (Jim Joe)
(Bob Ned Sue) (Don Pat) (Jim Joe Liz)
(Bob Ned Sue) (Don Liz) (Jim Joe Pat)
(Bob Ned Sue) (Don Joe) (Jim Liz Pat)
(Bob Ned Sue) (Don Jim) (Joe Liz Pat)
(Bob Pat Sue) (Don Jim Liz) (Joe Ned)
(Bob Pat Sue) (Don Jim Ned) (Joe Liz)
(Bob Pat Sue) (Don Joe Liz) (Jim Ned)
(Bob Pat Sue) (Don Joe Ned) (Jim Liz)
(Bob Pat Sue) (Don Ned) (Jim Joe Liz)
(Bob Pat Sue) (Don Liz) (Jim Joe Ned)
(Bob Ned) (Don Jim Joe) (Liz Pat Sue)
(Bob Liz) (Don Jim Joe) (Ned Pat Sue)
(Bob Sue) (Don Jim Liz) (Joe Ned Pat)
(Bob Pat) (Don Jim Liz) (Joe Ned Sue)
(Bob Ned) (Don Jim Liz) (Joe Pat Sue)
(Bob Sue) (Don Jim Ned) (Joe Liz Pat)
(Bob Pat) (Don Jim Ned) (Joe Liz Sue)
(Bob Liz) (Don Jim Ned) (Joe Pat Sue)
(Bob Ned) (Don Jim Pat) (Joe Liz Sue)
(Bob Liz) (Don Jim Pat) (Joe Ned Sue)
(Bob Ned) (Don Jim Sue) (Joe Liz Pat)
(Bob Liz) (Don Jim Sue) (Joe Ned Pat)
(Bob Sue) (Don Joe Liz) (Jim Ned Pat)
(Bob Pat) (Don Joe Liz) (Jim Ned Sue)
(Bob Ned) (Don Joe Liz) (Jim Pat Sue)
(Bob Jim) (Don Joe Liz) (Ned Pat Sue)
(Bob Sue) (Don Joe Ned) (Jim Liz Pat)
(Bob Pat) (Don Joe Ned) (Jim Liz Sue)
(Bob Liz) (Don Joe Ned) (Jim Pat Sue)
(Bob Jim) (Don Joe Ned) (Liz Pat Sue)
(Bob Ned) (Don Joe Pat) (Jim Liz Sue)
(Bob Liz) (Don Joe Pat) (Jim Ned Sue)
(Bob Ned) (Don Joe Sue) (Jim Liz Pat)
(Bob Liz) (Don Joe Sue) (Jim Ned Pat)
(Bob Sue) (Don Liz Pat) (Jim Joe Ned)
(Bob Ned) (Don Liz Pat) (Jim Joe Sue)
(Bob Jim) (Don Liz Pat) (Joe Ned Sue)
(Bob Pat) (Don Liz Sue) (Jim Joe Ned)
(Bob Ned) (Don Liz Sue) (Jim Joe Pat)
(Bob Jim) (Don Liz Sue) (Joe Ned Pat)
(Bob Sue) (Don Ned Pat) (Jim Joe Liz)
(Bob Liz) (Don Ned Pat) (Jim Joe Sue)
(Bob Jim) (Don Ned Pat) (Joe Liz Sue)
(Bob Pat) (Don Ned Sue) (Jim Joe Liz)
(Bob Liz) (Don Ned Sue) (Jim Joe Pat)
(Bob Jim) (Don Ned Sue) (Joe Liz Pat)
(Bob Ned) (Don Pat Sue) (Jim Joe Liz)
(Bob Liz) (Don Pat Sue) (Jim Joe Ned)
(Bob Don) (Jim Joe Liz) (Ned Pat Sue)
(Bob Don) (Jim Joe Ned) (Liz Pat Sue)
(Bob Don) (Jim Liz Pat) (Joe Ned Sue)
(Bob Don) (Jim Liz Sue) (Joe Ned Pat)
(Bob Don) (Jim Ned Pat) (Joe Liz Sue)
(Bob Don) (Jim Ned Sue) (Joe Liz Pat)

Group size template: 6 2
(Bob Don Jim Liz Pat Sue) (Joe Ned)
(Bob Don Jim Ned Pat Sue) (Joe Liz)
(Bob Ned) (Don Jim Joe Liz Pat Sue)
(Bob Liz) (Don Jim Joe Ned Pat Sue)

Group size template: 5 3
(Bob Don Jim Liz Pat) (Joe Ned Sue)
(Bob Don Jim Liz Sue) (Joe Ned Pat)
(Bob Don Jim Ned Pat) (Joe Liz Sue)
(Bob Don Jim Ned Sue) (Joe Liz Pat)
(Bob Don Liz Pat Sue) (Jim Joe Ned)
(Bob Don Ned Pat Sue) (Jim Joe Liz)
(Bob Jim Liz Pat Sue) (Don Joe Ned)
(Bob Jim Ned Pat Sue) (Don Joe Liz)
(Bob Ned Sue) (Don Jim Joe Liz Pat)
(Bob Ned Pat) (Don Jim Joe Liz Sue)
(Bob Liz Sue) (Don Jim Joe Ned Pat)
(Bob Liz Pat) (Don Jim Joe Ned Sue)
(Bob Jim Ned) (Don Joe Liz Pat Sue)
(Bob Jim Liz) (Don Joe Ned Pat Sue)
(Bob Don Ned) (Jim Joe Liz Pat Sue)
(Bob Don Liz) (Jim Joe Ned Pat Sue)

Group size template: 4 4
(Bob Don Jim Liz) (Joe Ned Pat Sue)
(Bob Don Jim Ned) (Joe Liz Pat Sue)
(Bob Don Liz Pat) (Jim Joe Ned Sue)
(Bob Don Liz Sue) (Jim Joe Ned Pat)
(Bob Don Ned Pat) (Jim Joe Liz Sue)
(Bob Don Ned Sue) (Jim Joe Liz Pat)
(Bob Jim Liz Pat) (Don Joe Ned Sue)
(Bob Jim Liz Sue) (Don Joe Ned Pat)
(Bob Jim Ned Pat) (Don Joe Liz Sue)
(Bob Jim Ned Sue) (Don Joe Liz Pat)
(Bob Liz Pat Sue) (Don Jim Joe Ned)
(Bob Ned Pat Sue) (Don Jim Joe Liz)

Solutions: 2589
posted by RichardP at 5:49 AM on October 11, 2005 [1 favorite]

Hmm... Metafilter cut off my post, it probably was too long. I've posted a text file containing the solution output from the perl code.
posted by RichardP at 5:55 AM on October 11, 2005

heh, when I first read this I thought you were trying to get us to help you with your LSATs. Nice job with the prolog, Andrew, I immediately thought of perl and would have missed the much more elegent solution.
posted by allen.spaulding at 6:18 AM on October 11, 2005

odinstream, you didn't take into account the HTML tags+line breaks which makes it ~32K.
posted by Sharcho at 6:26 AM on October 11, 2005

one extra point (since i may have been answering the wrong question) - did you mean that each "answer" had to include everyone?

richardp's code is giving all the different ways of dividing everyone up (so that everyone is in a group). what i was doing (or trying to do) was give you all the different groups, without worrying about people who weren't in any group.

do you see the difference? if you want "my" interpretation then richardp's output is too long (contains the right answers, but with many duplications). if you want "richard's" interpretation then my program didn't do the full job (and still doesn't run anyway!).
posted by andrew cooke at 6:28 AM on October 11, 2005

RichardP, you should probably be using Algorithm::Permute / Math::Combinatorics or something.
posted by Sharcho at 6:30 AM on October 11, 2005

Response by poster: Richard that really is above and beyond the call. I could say it was what I was looking for but at the risk of seeming ungrateful it is not exactly and that is my fault. I just re-read the question and it doesnt even read properly.

What I meant to ask is for a list of the distinct possible groups. i.e. all the possible groups with 1 member, 2 members through to 6 members order does not matter. [Bob Sue] and [Sue Bob] count as one.

If its not possible or easy. I can parse you result file and get the distinct groups or re-write you Perl in VB and adapt.

Thanks Ken

/On preview yes Andrew I wanted all possible distinct groups
posted by kenaman at 6:40 AM on October 11, 2005

Best answer: That is a good point Andrew. My code would be smaller and simpler if kenaman wants just a list of the legal groups instead of a list of legal partitions into groups. I've posted a text file containing the smaller solution output by the simpler perl code.

On preview: no problem, kenaman.
posted by RichardP at 6:50 AM on October 11, 2005

Sharcho, I'm sure you're correct, I would not be at all surprised if CPAN has something appropriate. However, since the task was so small and a one-off solution I'm sure it would have taken me longer to find an appropriate CPAN module and read the instructions on how to make use of it then the few minutes it took me to build some code that did a quick-and-dirty recursive exploration of the solution space.
posted by RichardP at 6:56 AM on October 11, 2005

Response by poster: Thats it Richard. That the answer I was looking for.

Many thanks for you time and effort.
posted by kenaman at 6:58 AM on October 11, 2005

Response by poster: you(r) time and effort!
posted by kenaman at 6:59 AM on October 11, 2005

It'd be interesting to see if someone can come up with the correct solution in prolog.. I wish I could but it's been too long :-/
posted by seinfeld at 7:44 AM on October 11, 2005

well i just heard back from my prolog guru (hi andreas!). he reckons the following should work, but it still zaps the stack for the prolog i'm using:

someone(sue).
someone(jim).
someone(pat).
someone(don).
someone(bob).
someone(joe).
someone(liz).
someone(ned).

enemy(bob,joe).
enemy(joe,bob).
enemy(liz,ned).
enemy(ned,liz).

group(G):-
group(0, [], G0),
sort(G0, G).

group(N, A, A):-
N >= 3,
N =< 7.br>
group(N, A, G):-
someone(S),
\+ member(S, A),
\+ (member(T, A), enemy(S, T)),
M is N + 1,
group(M, [S|A], G).

also, it's not as clear (at least to me) what the logic is. but i guess being right wins out over clarity.

anyway, instructions to run this, if anyone wants to give it a try:

stick the above in a file called mefi.pl
within prolog, type
consult('mefi.pl').
then type
group(G).
and keep hitting ";" for more values (it will print answers one by one. alternatively, type
setof(G, group(G), Z).
which is what overflows my stack. andreas says there are 109 groups.

disclaimer - he was in a rush and i've not had a chance to chat, so he may be answering yet another version of the problem.

and remember, those "." are needed - it's not just me adding anal punctuation to my post...
posted by andrew cooke at 3:56 PM on October 11, 2005

This really is simpler than a lot of these solutions are making it out to be. You just have to find all the groups of Sue, Jim, Pat and John, plus the empty group, of which there are 16 (just iterate through turning each person on and off), and then for each of those groups, you add Bob, Joe, or neither, and then Liz, Ned, or niether. Then you remove the entirely empty group, so you get 3*3*16-1 groups.
posted by cameldrv at 4:01 PM on October 11, 2005

sweet, cameldrv.

names = ["sue", "jim", "pat", "don", "bob", "joe", "liz", "ned"]

def show(n):
for i in range(len(names)):
if 2**i & n: print names[i],
print

def ok(n, i, j):

def main():
for i in range(256):
if i > 0 and ok(i, 4, 5) and ok(i, 6, 7):
show(i)

main()

stick that in mefi.py and type "python mefi.py".
posted by andrew cooke at 4:21 PM on October 11, 2005

for i in range(2**len(names)):

is a bit neater.
posted by andrew cooke at 4:23 PM on October 11, 2005

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