snake_upper_bound

An upper bound of the maximal length of the longest snake in a box is given by $$ 1 + 2^{n-1}\frac{6n}{6n + \frac{1}{6\sqrt{6}}n^{\frac 1 2} - 7}. $$

theorem snake_upper_bound (n : ℕ) : LongestSnakeInTheBox n
    ≤ (1 : ℝ) + 2 ^ (n - 1) * (6 * n) / (6 * n + (1 / (6 * √6) * √n))

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