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Great game idea! It sort of sounds like the game I submitted for last years contest called Bleap. Here is that game for inspiration or some more brainstorming. https://github.com/CDNSpeedGames/2017/releases/tag/Bleap.v1.0

I think your game belongs to the genre 3D platsform/puzzle.  I do not know what genre the game I am about to make belongs to, but it is not a platform/puzzle game. 

But of course I could later on add puzzle moments to the game