GCRhoads just sent an e-mail to the OHEX mailing list with the solutions to 7x7. It had some results that were fairly surprising, The moves that should be swapped were not as many as many people thought…..The moves that should not be swapped on 7x7 are the following: A-F1, A2, B2, D2, A3, and A5 and they're equivalent rotated moves…I'll take those 10 euros now yper :)…anyway, i know the opening moves and swapping topic got about 25 posts, so i know there's some interest in this…marius, be careful about genaralizing these results though, because i suspect that there is a more complicated set of non-swapping moves for 13x13…good luck

A-F1 do you mean A1-B1-C1-D1-E1-F1 or A1 and F1?

i meant A1, B1, C1, D1, E1, F1

I'll be careful :-) However, I can't help myself, and have to try. I've looked at 3x3, 4x4 and 5x5, and it seemed to me that an opening move which was losing in one size always is losing in a larger board. I believe this to be the case, even though I've not seen a proof for it. Anyone know if there is one? I might be willing to accept that this is not the case when you go from an odd to an even board or vice verca (from 6x6 to 7x7, for example). Tray, if you could find the losing move for 6x6 also, we could at least check my hypothesis in boards 1x1 to 7x7?

Refusing to yield - Marius :-)

I'm afraid your hypothesis doesn't hold, Marius. B2 is losing on size 4, but winning on size 5 and 6. A3 is losing on size 4 and 5, but winning on size 6.

For the complete results up to size 6, go to Queenbee's homepage.

i've been looking at the general solution for smaller boards too, and i saw this…

3x3 9 opening moves/4 lose

5x5 25 opening moves/12 lose

7x7 49 opening moves/24 lose

am i the only one that sees a continuancy?

for the ones who don't see it, if board is (2n+1)x(2n+1) there are n losing opening moves.

actualy works for the 1x1 board too

1 possible move/0 losing moves …

grr, and sorry for the spam but if B(oardsize)=(2n+1)x(2n+1) then the amount of losing moves is (B-1)/2 and not n as i earlier insinuated…

Or to put it another way, the number of winning moves is one more than the number of losing moves.

An interesting theory, but I find the number of losing moves on a 7x7 board to be only 22.

when i drawed a board and noted the losing moves i wrongly wrote down A4 as a losing move too…i'm sorry for the missunderstanding…in the smaller boards the losing moves are grouped together (split by a groupe of winning moves), here there seems to be an isolated point A5 (G3)

OK, now: If there's a system here at all, it seems to be pretty complicated. But one thing at least seems to be systematic: In an nxn board, opening moves a1-(n-1)1 are losing moves while (n)1 is a winning move. It also seems that, at least on a “large” scale, the number of other losing moves are incricing with increasing board size (not very surprising, is it?). Ofcourse, determining WHICH moves are losing is still the problem, and since they aren't even connected in 7x7, I suppose drawing conclusions like “a3 and b2 are both probably losing in 13x13, since they are so close to the corner and ther must be many losing move” are really way beyond line. Is 8x8 solved in the same manner yet, by the way?

Yes.

http://www.ee.umanitoba.ca/~jingyang/hex88-1.html

The program at the site only shows a winning strategy of 8x8 hex if it's allowed to start in the “centre”. It doesn't know if a given opening move, say b2, is winning or losing.

Of course. My mistake. :)

Can any one give a link to the 7x7 solution?