Judithkcg@aol.com wrote:
> OK, here I am bothering you again.  I have made a spread sheet with the 
> groupings that you gave me and showing that the first letter of each group is 
> host (#1) . Each couple is hosting 2 times a year........Is it possible for 
> your formula to indicate a #2, #3,& #4 in each group ending up with each 
> couple having 2 of each throughout the 8 months?.......I can make it work 
> until the last 2 months and then my combinations overlap........any ideas???  

Okay, a few more minutes of coding, a few more hours of cpu,
and I have a new chart with each couple playing each "role"
exactly twice.  Of course, these are pretty hefty requirements
(as you discovered), so the solution isn't as great in terms
of meeting all the couples.  Some couples now only meet 18
other couples, but that's the best it could do.

BTW, hopefully you understand that the perfect solution is
unattainable.  It *seems* like you can meet 3 other couples
each month and meet them all in 8 but it doesn't work when
you actually try it.  This solution is a long way from the
perfect solution, but I challenge you to find a solution
that is even slightly better and still meets the other
goals.  Of course if I relax any of the requirements I can
do much better on the other goals.
--
Paul Chamberlain, tif@tifster.com


In the chart, each letter is a couple.  Each grouping
meets together.  The first couple in each group would
be the host, the second couple would bring desert, or
whatever, etc.  Each line represents one month's dinners.

MCHK LRDW UQVX AFPB JOST INEG
NXHB TQAV LKEJ DSUF PWIC RGOM
OIKU AMSE WJQH GVBD NPFL XCTR
DJVP KIXA OHMN FTGL REUQ BSWC
KUWT EHXP FBRO CAQG SLNV IDJM
HKTS EDCO VXFW JRNA QLBI MGPU
GWAS CUJN QFKD BTME HVIR POLX
WEOF TNDI SPRQ UALH XBGJ VMCK


This chart represents the number of times each couple
eats with each other couple.  Each couple meets at
least 18 others and some do as well as 22.

  A B C D E F G H I J K L M N O P Q R S T U V W X
A . 1 1 0 1 1 2 1 1 1 1 1 1 1 0 1 2 1 2 1 1 1 1 1
B 1 . 1 1 1 2 2 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 2
C 1 1 . 1 1 0 1 1 1 1 2 0 2 1 1 1 1 1 1 1 1 1 2 1
D 0 1 1 . 1 2 1 0 2 2 1 1 1 1 1 1 1 1 1 1 1 2 1 0
E 1 1 1 1 . 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 0 1 1
F 1 2 0 2 1 . 1 0 0 0 1 2 0 1 2 2 1 1 1 1 1 1 2 1
G 2 2 1 1 1 1 . 0 1 1 0 1 2 1 1 1 1 1 1 1 1 1 1 1
H 1 1 1 0 1 0 0 . 1 1 2 1 2 2 1 1 1 1 1 1 1 1 1 2
I 1 1 1 2 1 0 1 1 . 1 2 1 1 2 1 1 1 1 0 1 1 1 1 1
J 1 1 1 2 1 0 1 1 1 . 1 1 1 2 1 1 1 1 1 1 1 1 1 1
K 1 0 2 1 1 1 0 2 2 1 . 1 2 0 1 0 1 0 1 2 2 1 1 1
L 1 1 0 1 1 2 1 1 1 1 1 . 0 2 1 2 1 1 1 1 1 1 1 1
M 1 1 2 1 2 0 2 2 1 1 2 0 . 1 2 1 0 1 1 1 1 1 0 0
N 1 1 1 1 1 1 1 2 2 2 0 2 1 . 1 1 0 1 1 1 1 1 0 1
O 0 1 1 1 2 2 1 1 1 1 1 1 2 1 . 1 0 2 1 1 1 0 1 1
P 1 1 1 1 1 2 1 1 1 1 0 2 1 1 1 . 1 1 1 0 1 1 1 2
Q 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 . 2 1 1 2 2 1 1
R 1 1 1 1 1 1 1 1 1 1 0 1 1 1 2 1 2 . 1 1 1 1 1 1
S 2 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 . 2 1 1 2 0
T 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 0 1 1 2 . 1 1 1 1
U 1 0 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 . 1 1 1
V 1 1 1 2 0 1 1 1 1 1 1 1 1 1 0 1 2 1 1 1 1 . 1 2
W 1 1 2 1 1 2 1 1 1 1 1 1 0 0 1 1 1 1 2 1 1 1 . 1
X 1 2 1 0 1 1 1 2 1 1 1 1 0 1 1 2 1 1 0 1 1 2 1 .


This chart represent the number of times each couple
cooks for another couple or is cooked for by that
couple.  Note that no one ever cooks for somebody twice.
In fact, just because of the way I did it, you also
don't ever get hosted by someone you hosted.

  A B C D E F G H I J K L M N O P Q R S T U V W X
A . 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0
B 1 . 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1
C 1 1 . 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1
D 0 0 0 . 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0
E 1 1 1 1 . 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1
F 1 1 0 1 0 . 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0
G 1 1 1 1 0 1 . 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1
H 0 0 0 0 1 0 0 . 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0
I 0 0 0 1 1 0 1 1 . 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0
J 1 0 1 1 0 0 0 0 1 . 0 1 0 1 1 0 0 1 1 1 0 0 1 1
K 1 0 0 0 0 0 0 1 1 0 . 1 1 0 1 0 1 0 0 1 1 1 1 1
L 0 0 0 1 1 1 0 0 0 1 1 . 0 1 0 1 1 1 1 0 1 0 1 0
M 1 1 1 0 0 0 1 1 1 0 1 0 . 0 1 1 0 1 0 0 1 1 0 0
N 0 1 1 0 0 1 0 1 1 1 0 1 0 . 1 1 0 0 1 1 0 0 0 1
O 0 0 0 0 1 1 0 1 1 1 1 0 1 1 . 1 0 1 0 0 1 0 1 0
P 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 . 0 0 1 0 0 0 1 1
Q 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 . 1 1 1 1 0 1 0
R 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 . 1 0 1 0 0 1
S 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 . 0 0 1 0 0
T 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 . 0 1 0 1
U 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 . 1 0 1
V 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 . 1 1
W 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 . 0
X 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 .

This chart represents the number of times each couple
plays each role (host, desert, etc.)  Some of the
solutions weren't perfect in this regard, even though
this one is.

  A B C D E F G H I J K L M N O P Q R S T U V W X
a 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 
b 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 
c 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 
d 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2