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How to come up with ame mechanics ideas? Play games, start with something small, copy things that work from others. Experiment, and iterate on your idea until it's great.
https://www.rockpapershotgun.com/2015/01/22/how-to-make-a-puzzle-game/
Six tips on how to build a good puzzle game, including: helping the player along, learning over solving, exploring level designs, keeping the design streamlined and minimalism, and the role of a central game mechanic that everything contributes to.