I was thinking about Oekaki puzzles last night. I was trying to decide if it was possible to design one with multiple solutions.
I figured out it was fairly easy to design some puzzles that multiple solutions that were reflections of each other, but I wasn’t able to figure out any that had more than one non-reflective solution. Is it possible?
Oh yes, I also quickly realized it was easy to figure out simple oekakis that had numerous solutions like puzzles with 1-1-1-1-1 horizontal and vertical series.
You’ve surely found trivial examples, like a 2x2 grid with 1 on each row and column. Now take any more complicated picture, and stick one of those in isolated from any of the other filled-in areas. Presto, your more complicated picture also now has multiple solutions. There are also some more complicated ambiguities, where you can’t tell something like
o o
oXXXXXoo
X X
X X
ooXXXXXo
o o
from
o o
ooXXXXXo
X X
X X
oXXXXXoo
o o
where the Xs are filled in, the os are empty, and all the other squares could be anything at all. I even once saw one in GAMES magazine which had two possible solutions, this way (though from the picture, it was clear which one was “correct”).
The problem is, if dont get it all just right, you will have a picture that doesn’t look just right.
Symetery does help in some of the puzzles, but I would say enough of them avoid it, as not to give any clues at all.
Glad to see that people are finally moving away from Sudoku and Karuko.
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