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Very neat toy! I was only able to solve 1-4, and I did so just by stumbling around. I imagine it's difficult to tutorialize. It took me a bit to figure out that every hat has 2 children (even the ones that look like they would have 1 or 3 children), and that recursion depth is 8. Very fun to play around with though!

Ideas that popped into my head:
- I wonder if hats becoming darker/lighter/more transparent as they get further from the source would be a helpful visual
- I wonder if a UI element indicating the order of the 8 hats that are actually used would be helpful. (Or, a customizable slider for the recursion depth, between 3 and 8)