Something that we've been using => Answer Key : Enter the number of horizontal and/or vertical double bridges
But it is bit error prone, and may be gusseable

No of single bridges and double bridges in selected rows/columns. The rows/columns need to be selected carefully. Perhaps we'll need to specify at least 3 rows/columns to ensure that solvers solve it completely.

For last row answer will be (3,1) and for last column (1,3)

Seems good.

That also seems very guessable, at least for that row. I'd probably suggest marking a line that runs in between the digits. And then indicating the sections of bridges you encounter with either 1 or 2.



Like this, with the answer code being 11212121, 222212.
Didn't check if this was the best place to choose from the design, just seemed like a place where the bridges in some places are not there, even they could technically be possible.

I like Para's suggestion very much.

I like this suggestion too. But I have a couple of points:

1. Are the 'arrow lines' to be given drawn as part of the puzzle?
2. If not, it 'may be' difficult to imagine a straight line if the distance between unit circles is very less. For argument sake, suppose you wanted the column arrow to be between the last two '4's of the 1st row. How would you ensure its not inconvenient for the player to assess?

If these small problems can be sorted out, then this is the best answer key for sure.

If there is no natural space in the puzzle for the two arrows, you can just reformat the grid with an extra gap. I definitely like this arrow line idea.

Then this will be a very convenient and easy answer key. Definitely easier than counting double bridges.

Since this was just linked from the PR 2020 discussion: https://logicmastersindia.com/forum/forums/thread-view.asp?tid=2737#...

Just want to note one downside of this suggestion, compared to the version used on PR (which was to ask for a sequence of N numbers 0/1/2 counting the "horizontal" bridges in a row of N+1 clues). Namely, that the suggestion here has no fixed length. Some form of checksum like a fixed length or sum is very useful to avoid typos.