Candledave, Buzzb - the wheels of logic have creaked around in the rusty iron difference engine that is what remains of my brain, and now I fully understand why the three remaining family members just couldn't participate, given the thematic rule.
Put it down as a special macro example of the Exclusion Principle.
Interestingly, the family dog, lately cast out of the household apparently because it hadn't kept its part of the garden tidy,
would have qualified.