It would seem to make sense for the middle n to be false, but the details seem elusive.
With n=1 the system is paradoxical, with the first statement claiming the second to be true while the latter claims the first to be false.
For n=2 it does seem the middle two are false while the first and last are true.
For n=3 it is still the middle 2 that are false while the top two and bottom two are true.
With n=4 it seems paradoxical again with the first and last two seeming to be true and the middle two seeming false, but the 3rd and 6th flipflop endlessly, with no stable equilibrium.
For n=5 the middle 4 are false while the first 3 and last 3 are true.
For n=6, the first and last 4 are true and the middle 4 are false.
It would seem that in the limiting case, the top and bottom thirds (2n/3) are true while the middle third are false, but when n is not divisible by 3, the list is sometimes paradoxical and at other times something close to division into thirds.

Posted by Charlie
on 20121207 16:59:56 