Residue Kaleidoscope

Turn the dial freely. The verdict remembers every turn.

Every draw becomes a colour recipe. You may inspect moduli 2 through 10; the omnibus reading corrects the smallest p-value across that whole menu.

Compositions modulo 2

Euro Millions Plus5/50 era · since Sep 2024206 draws

Pool by residue: 25 · 25
Displayed χ²: 8.65
Displayed raw p: 0.124
All-moduli p: 1.000

[2, 3]60 / 67.1

[3, 2]63 / 67.1

[1, 4]31 / 30.7

[4, 1]39 / 30.7

[0, 5]10 / 5.2

[5, 0]3 / 5.2

Finite-pool compositions + family correctionresidue-suite-v1exact cells; pooled χ²; Bonferroni over moduli 2–10

The maths, in plain language

A finite-pool colour recipe

If residue $r$ owns $n_r$ balls and a draw contains $c_r$ of them,

$P (c_{0}, \dots, c_{m - 1}) = \frac{\prod_{r} (\binom{n_{r}}{_{}}}{}$

The story behind it

The pattern a partition creates

Modular patterns feel structural because they repeat visually. But a partition creates its own shapes before a draw happens. The kaleidoscope separates those lawful shapes from deviations in the history.