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 flip-flop 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 2012-12-07 16:59:56