Setting up playgroups

I don't think this is really an excel or vba question, more of a general question about an algorithm. The problem you describe is non-trivial and related to the social golfer problem which has been proven to be NP-complete, so very difficult to solve for larger amounts of people/groups.

For your parameters, the social golfer problem in its original form (no two people can ever be in the same group twice) is obviously unsolvable, so you have to specify what you want "minimum overlap" to mean. It can either mean "maximize the number of overall contacts" so every child should be in the same group with every other child at least once. This seems achievable pretty easily with your parameters.

Alternatively you can try to minimize a "penalty score" aka each child should be in the same group as every other child at least once, but not more than once. Being in the same group two or more times will increase the "penalty score" which you try to minimize. This is certainly a valid option for your problem.

Luckily there is a website that allows you to determine a schedule just like this, however, it can't fulfill your requirement of an even boy/girl distribution. The website can be found here: https://goodenoughgolfers.com/

I once wrote a solver for this problem myself, including the boy/girl distribution requirement, but it is still very bare bone and just available as source code in c++ here.

I computed the following distributions with my tool and adapted the result manually to fit your criteria:

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Well, set this up as a basic control. You can add extra constraints as you need, such as controlling the number of M and F in each group, be good practice for you.