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once you've played mathemagic, you have all the information you need to solve the cabinet under the fish tank. (hint- pay attention to what happens when you defeat the enemies!) from there, the planet puzzle will make more sense

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i did it, but does something happen when you do it, and how do i get the swan piece, and if anything, am i missing something?

mathemagic doesn't give you anything for beating it, but by beating it, you learn what the symbols mean. There are 5 symbols. These are the same symbols on the cabinet below the fish tank. The fishtank cabinet has 3 equations. each of those equations needs to be valid (8 / 2 = 4, for example)