Jonny,
Just to let you know that I have modified the title to distinguish this thread from another with the same name.
It is possible to have an optimal schedule here, where every couple meets 14 of the other couples exactly once, and the remaining 5 couples exactly twice. So I think the following schedule should work well for your bridge group. The 20 couples are labelled A to T. I have tried to leave as much time as possible between the two occasions when a couple hosts, with a break of at least two rounds between occasions.
Round Group 1 Group 2 Group 3 Group 4 Group 5 Hosts
1 (A C D R) (E G O Q) (H I K N) (B F L M) (J P S T) [C G I L T]
2 (A I M T) (B E K R) (D H P Q) (C F N O) (G J L S) [A B D N S]
3 (D J K T) (B F O S) (C E I P) (A L N Q) (G H M R) [K O P Q R]
4 (E I R S) (A F G P) (H O Q T) (B C J N) (D K L M) [E F H J M]
5 (A K Q S) (B D E G) (F H I J) (C L R T) (M N O P) [A G I L N]
6 (B J M Q) (C F G K) (A D I O) (N P R T) (E H L S) [B C O P S]
7 (A E J N) (K L O P) (C H M S) (D F Q R) (B G I T) [E K M R T]
8 (D G N S) (E F M T) (A B H P) (J K O R) (C I L Q) [D F H J Q]
Jonny,
I thought some more about this schedule and noticed that there are 4 couples who at some point return to the same host. The worst is couple L, who go twice to both Q and S. That prompted me to look for a better assignment. So if there is still time, then I suggest you replace the 'Hosts' matrix above with:
[A E N M J]
[T K H F G]
[D S C Q R]
[I P O B L]
[K G J T M]
[Q C D N E]
[A P H R I]
[S F B O L]
For these new host assignments, I have written down the schedule of who goes to which home in which round. Below an asterisk indicates that a couple hosts.
1 2 3 4 5 6 7 8
----------------
A | * T Q P K D * B
B | M K S * G Q I *
C | A F * B T * H L
D | A H * L G * R S
E | * K C I G * A F
F | M * S P J C R *
G | E * R P * C I S
H | N * R O J E * B
I | N T C * J D * L
J | * G D B * Q A O
K | N * D L * C P O
L | M G Q * T E P *
M | * T R L * Q H F
N | * F Q B M * A S
O | E F S * M D P *
P | J H C * M N * B
Q | E H * O K * R L
R | A K * I T N * O
S | J G * I K E H *
T | J * D O * N I F
This makes it easy to check that all couples host twice and get to go to six different homes. Hope that helps,
Ian.