Analysing groups of cells to form new groups

HI
I have been directed here by someone who tells me this is the griendliest and most helpful Excel there is so here goes

What I have is a group of 16 people who have to be arranged into 4 groups of 4 on 5 different occasions.

My task is to organise the final (5th) groupings. The previous 4 sessions groups have been pretty random, and they will not always follow the same patterns on subsequent courses.

What I want/need to do is try to ensure that everyone, after my session, has been in a group with as many of the other people as possible while at the same time minimising the number of "double ups".

I am hopeful that someone can come up with a solution, otherwise I am back to my previous method that involves a pad and pencil and a whole lot of hope

I attach the data I am trying to work with.

Thanks in advance.

....and, of course, that first sentence should real "I have been directed here by someone who tells me this is the friendliest and most helpful Excel forum there is so here goes"
Sorry....

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