What is the name of this game? And what type is it?

single-word-requests

These are sliding puzzles.


The "15 puzzle" since in the 1880s popular version the tiles were numbered 1 to 15 ... LINK
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In French we call it Jeu de Taquin.

This name is internationally (so in English) used by mathematician to describe problems similar to the one your game raise.

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