Theory behind a logic puzzle ?

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I am helping my children with a computer game based on Logic and Reasoning. The player has to solve different puzzles as the game progresses. I am struggling with a matching puzzle where the player has to form a string of the game characters based on their traits. Please see the attached file for a snapshot of the puzzle. I am not sure how I should approach such a problem. I also wish to know the branch of Mathematics that studies this kind of problems.

Brief background. The characters in the game are called Zoombinis, with each of them having four special characteristics : hair, eyes, nose, and foot. Based on 4/5 variations of the each of the charactristics, the game randomly produces zoombinis. The player has to guide around 16 zoombinis at a time through various puzzles.

At the above mentioned matching puzzle, the game produces a string of holes (where one zoombini can be placed) . Between two holes a picture of one of the 4 characteristics is shown. The two zoombinis on the either side of a picture have to have the same trait. For example, if there is an eye picture between two holes, then the zoombinis on the either side of that picture have to have similar types of eyes; both of them can have sleepy eyes, or wide-open eyes, or eyes covered with glasses.





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As the title you mentioned, Logic and Reasoning, suggests, this game appears to get the child used to isolating features out of a set of features, a skill used in much of reasoning. If you wanted to formalize it, either for yourself or for the child, you could approach it, for example, with Venn Diagrams from set theory. If you wanted to get a little more complicated, then you could introduce "equivalence relations" and "equivalence classes".


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The original post appears to be 10 years old! The kids have probably grown up by now.


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Oops o:). I didn't notice the date; it just showed up on a list of questions with "0 replies" next to it. Ah, well, maybe like in Peter Pan, the kids can teach their kids....
The original post appears to be 10 years old! The kids have probably grown up by now.
Thanks folks. Indeed, the kid who was working on that puzzle will be going to university this fall to study Mathematics!

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