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Puzzling

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    $\begingroup$ I believe the point of Lezzups answer is that there's 24 ways to fill out the numbers in the yellow, green, and red squares, and pretty much any of them is valid. So there's ~13824 solutions, not just this one. $\endgroup$
    – Mooing Duck
    Commented Jul 21, 2023 at 20:42
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    $\begingroup$ I think there are a lot more than that, @MooingDuck. Lezzup effectively divides the 16x16 grid into 16 independent 4x4 puzzles, split evenly among 4 color-coded categories. With 288 distinct 4x4 sudoku (including label permutations) that makes for 288^16 total ways to fill out a Lezzup-style grid. Even if you divide by the 16! permutations of the labels, that still gives you about 10^26 solutions of this form. $\endgroup$
    – John Bollinger
    Commented Jul 23, 2023 at 15:10
  • $\begingroup$ Or perhaps that's a generalization of what Lezzup had in mind, but it's true in any case. $\endgroup$
    – John Bollinger
    Commented Jul 23, 2023 at 15:22
  • $\begingroup$ Ah. There are 13824 solutions where all the pink squares are identical, all the green, all the yellow, and all the grey too. But you're right that there's many more where they aren't identical. I'd overlooked those. $\endgroup$
    – Mooing Duck
    Commented Jul 23, 2023 at 18:48
  • $\begingroup$ @JohnBollinger Initially, I wanted to create not just one example, but a nice pattern to simplify the proof how it could be possible. Turns out, that the pattern was very elegant and symetrical. However, I didn't thought about how many solutions it had, but 10^26 is mindboggeling! Thanks for calculating! $\endgroup$
    – Lezzup
    Commented Jul 24, 2023 at 13:32