Strip the outer shell off a ten-by-ten-by-ten block of unit cubes and count what falls. The reflex answer, 271, is arithmetic done correctly on the wrong picture: a shell leaves from both opposing faces, so every axis loses two units and not one. Two independent counts land on 488, and the general shell turns out to grow like a surface rather than a volume.
One condition, a two-line recurrence, and the fifth power falls out as a clean 123 with no radicals left. Climb the same ladder far enough and the golden ratio and the Lucas numbers are hiding underneath.
Infinitely many lines separate the same data; only the widest street generalizes. And once it's found, almost none of your points were holding it up.
A line with rational coefficients maps ℚ onto ℚ. Nothing curved ever does. Three filters — interpolation, shape, denominators — leave the full classification.