Yes. And. Hell. Yes.

If you pull that off, you're a shoe-in for a Golden Shoehorn Award.

If down the road, nth-cousins mth-removed that happen be descended from the double cousins marry and have a kid, and you put that child at the top of the tree in the diagram, the four parents of the brothers who married the sisters will occupy eight slots on one generation of great-...-grandparents. I think.

I don't think it changes the genealogical tree looking back in time until the loop gets closed, but it's late and I've used up all my thinking ability for the day. Time to go write some code.

Also, the other way to look at it is that there are 2^(n+2) (great-)‧n-grand{ma|pa} states, but due to population constraints, they're degenerate, and you'll have the same person filling multiple (great-)‧n-grand{ma|pa} states, possibly for multiple values of n. Probably no more than ±1 of the median n value†. Also, the degeneracy is most likely to occur only for n > 2 (so you don't have to worry about the grand{ma|pa} and {ma|pa} states being degenerate in the overwhelming majority of cases).

† See P161911's post below for relevant genealogical implications of this situation.

Awesome write up. Unfortunately, that sounds a little too much like my cylinder head swap job... Next time I have to do any surgery in the engine bay, I'm going to a shop to get the A/C depressurized, and then I'm going to yank it and sell it. Bloody useless thing, and the hard lines get in the way of everything. Those were the main obstacle for getting the head out.

I still haven't admitted to anyone on here what bits of bodging I pulled on the cylinder head job...

It's no fun being a jerk on the internet if you're actually right (I figured stacking all the greats on made for typesetting problems)...

This might make it easier: http://en.wikipedia.org/wiki/Finger_binary

Cute. Wrong, but cute. You only get 536,870,912 Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Great-Grandmas if the family tree only forks. Due to that 400,000,000 population constraint as you go back and the fact that the inbreeding taboo only applies to immediate family and (depending on culture) first cousins, you will get loops in the tree as you look backwards.

So. The real tag line is: You're related to everyone, twice, and yer all INBRED!

(Also: perl -e 'print "Great-"x28,"Grandmas"', copping out with the '...x30' is lazy. Or at least, the wrong kind of lazy... ;)

The Rosenbergs?

SBF powered Locost. I intend to do this by the end of the decade.