How Discrete Mathematics is used in Game Development

Party games

D_n = n!\sum_{k=0}^{n}\frac{(-1)^k}{k!}, \qquad \frac{D_n}{n!} \to \frac{1}{e}

Inclusion–exclusion and derangements

H_n = 2H_{n-1} + 1,\;\; H_1 = 1 \quad\Longrightarrow\quad H_n = 2^n - 1

Recurrence relations and induction

D_n = n!\sum_{k=0}^{n}\frac{(-1)^k}{k!}, \qquad \frac{D_n}{n!} \to \frac{1}{e}

Inclusion–exclusion and derangements

H_n = 2H_{n-1} + 1,\;\; H_1 = 1 \quad\Longrightarrow\quad H_n = 2^n - 1

Recurrence relations and induction