D³ · A₀ = dr(N) · Deterministic Data Decomposition

Amount N (cents)

—

A₀ = N mod 9

—

Ankerwaarde

Digital Root

—

dr(N) = A₀

Optimal Payment (Greedy — provably optimal) Canonical

Total Payment Ways (15 denominations) O(1)

—

Reduction Chain N → digit sum → … → dr(N)

Stelselparameters (p, q, r, s, t) — randvoorwaarden: p ≡ 1 (mod q) & t | s | r | q

p (layer A)

q (layer B)

r (layer C)

s (layer D)

t (layer E)

Quick:

A · p=19 · €100/200/500 + B · q=9 · €10/20/50 + C · r=3 · €1/2/5 + D · s=3 · €0,10/0,20/0,50 + E · t=1 · €0,01/0,02/0,05