As I mentioned in the other recent puzzle thread, when I computer-analysed

the 3x2 corner there were two endgames for which the winning moves weren't

what I would immediately have guessed. I posted one already; here's the

other (I mentioned this position in the previous thread). The reason

I didn't initially post this one was that this time blue has two winning

moves. Can anyone spot either of them? Blue to move: he's 10-7 up but

again stands to lose a lot of the 3x2 corner, especially if it turns

into a long chain.

6 + + +-+-+-+  |   |b|b|r|5 +-+-+-+-+-+  |r|b|b|b|r|4 +-+-+-+-+-+  |r|b|b|r|b|3 +-+-+-+-+-+        |r|r|2 + + + +-+-+        |b|b|1 + + + +-+-+  a b c d e f

For background as to how this puzzle arose see the other puzzle thread.

wc

PS @sam: regarding the “level” of this puzzle: I would *guess* that a typical 2000 player could just sit down and work out the answer with pencil and paper and brute force but that a typical 1700 player might not be able to do this accurately enough to really prove that the answer they gave really worked. This might however be because a typical 1700 player might not have the time/energy to spend 30 minutes on one move in a game of dots and boxes!

Blue can win if he a) makes a loop or b) allows Red to get a chain in the south, but picks up a box there. So a2-a3 and b1-c1 are both winning moves for Blue.

Actually, there are lots of “transposes” between the two lines of play – checking one of them gives you a lot of information about the other.

WC: I think that giving a level for the puzzle is very useful!

@sam: correct and well done! I can quite believe you're right about the lines going into one another: after 1. a2-a3 2.b2-c2 blue's only winning continuation is 3.b1-c1. Conversely, after 1.b1-c1 (threatening the dreaded half-quad) a natural response for red is 2.b2-c2 and then the only winning move for blue is 3.a2-a3 etc. Somehow that's the trick—threaten the loops to force red to sacrifice for his chain.

wcc

I just realized that I've asked for a “level” in every thread. Very annoying of me. I'll stop doing that.

Maybe it would be good if it was in the thread title, too, something like “another 2x2 puzzle - level 1700-1800”

about levels: see my comments in the 2x2 position.