The Euro System as a (19,9,3,3)-System

What it does

The entire system can be written as a single formula: N = 19A + 9B + 3C + 3D where A, B, C, D count the denominations in each layer. The coefficients 19, 9, 3, 3 are not arbitrary — they satisfy 19 ≡ 1 (mod 9), and each divides the next. For any amount N (in units of €0.10), the minimal starting value is always: A₀ = N mod 9 Computed in O(1).

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