couples

gistfile1.txt

Q: i want to choose 4 people out of 4 couples. i want a group with at least 1 couple.

4 couples:
  ab
  cd
  ef
  gh

non-couples:
  6:a(c,d,e,f,g,h)
  6:b(c,d,e,f,g,h)
  4:c(e,f,g,h)
  4:d(e,f,g,h)
  2:e(g,h)
  2:f(g,h)
  --
  24

  pre-selecting one couple reduces # of selectable non-couples to 12.

couple(couple):
  3:ab(cd,ef,gh)
  2:cd(ef,gh)
  1:ef(gh)
  -
  6

for each couple:
  couple(12 non-couples + remaining selectable couples)

15:ab(12 + 3)
14:cd(12 + 2)
13:ef(12 + 1)
12:gh(12)
--
54
==