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My daughter (pre-school) had to solve the following puzzle:

puzzle

It consists of 9 square pieces and the goal is to fit them together in such a way that all inner (i.e. touching) sides show a valid, put-together pattern.

What is this type of puzzle called?

Is there a logical or even programmatical way (that is, not brute forcing it) to solve this type of puzzle?

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This is probably simply called an edge-matching puzzle (also known by various names such as Tetravex). The puzzle is in general NP-complete (i.e. not easy to solve in general cases), but the algorithms for solving do exist (e.g., Douglas-Rachford algorithm, but unfortunately I don't know the details).

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    $\begingroup$ Rob Stegmann's Puzzle Page shows many of these puzzles, including many variations with 3x3 square tiles, and has a bit of history of such puzzles. $\endgroup$ Mar 25 at 12:22

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