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Little Nemo
01-18-2007, 10:47 PM
I was thinking about Oekaki (http://en.wikipedia.org/wiki/Paint_by_numbers) 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?

Little Nemo
01-18-2007, 10:49 PM
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.

Chronos
01-18-2007, 11:29 PM
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 ofrom o o
ooXXXXXo
X X
X X
oXXXXXoo
o owhere 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").

Meeko
01-20-2007, 06:07 PM
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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