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Here is a gameboy game I used to play religiously as a teen , Final Fantasy Legends 2. In this game you end up traveling worlds back and forth , and in one world you have to solve some riddles of mysteries of 3 diff areas. One area is the cave of wind (I think) and the other 2 are an underwater volcano and a cave of light.
The cave of light is one of the sickest dungeons in the game and it has (surprise!!!!) checkered floors
skip through this youtube to see the cave of light (near the end)