I have created 3 Twixt puzzles in the same style as

Alex Randolph's 40 quarter-board puzzles, except that I have not yet posted the answers. That's up to you. I want to test how difficult they are, and whether they are fair. I think that all 3 are moderately tricky, and that they each have exactly 1 right answer. These are based on actual situations I got myself into.

Puzzle #1

White to move

Puzzle #2

White to move

Puzzle #3

White to move

I have a question about the object in these puzzles. In the Randolph series, the object for White is to connect any white peg in row 1 to any white peg in row 12, with the restriction that all pegs played must be inside the 12x12 region shown. For example, if white connects row 1 to a peg on B12, then white has achieved the object, even if black has a peg on C11 (which is connected to row M) and would be able to link to B13 (outside the region shown) on the next move. Similarly, if black connects row A to a peg on L2, White loses, even if white has a peg on K3 (which is connected to row 12) and could link to M2 on the next move. Does the same object apply for these puzzles?

When I was designing the puzzles, I was vaguely aware that there may potentially be anomalies in showing only 1/4 of a board. That is probably why I left a black link going off the side of the board on all 3 of these puzzles - something that Alex Randolph did not do. But I think these puzzles are safe from the condition you mention (aren't they?). In all 3 of them, I have a white peg on row 12, and a black link going off the right side of the board, and the assumption is that if you can connect the edge to that, then you've won. Thanks for the question, though.

You mention a black link going off the edge of the board, supposedly to avoid certain anomalies, but I don't see what sort of anomalies this black link would serve to avoid…? Anyway, if the object is for white to connect to the existing white peg on row 12, the puzzle should explicitly say so. I messaged you some specific variations.

By the way, thanks for posting these! They were fun to work on.

I wouldn't want to spoil the puzzles for anyone else, but after discussing the puzzles, Alan and I agree that:

Puzzle #1 does indeed have a unique winning first move.

Puzzle #2 has at least three winning first moves.

Puzzle #3 also arguably has more than one winning first move, but this can be “fixed” by adding a black peg on C11. That should leave just one solution, which was the intended solution.

CAVEAT: maybe we're wrong…