Maps with Bounded Stretch

★ 6/10combinatorics functions Counting Casework

Problem

Let $A = \{0, 1, 2, 3, 4, 5, 6\}$ , and let $f$ be a function from $A$ to the integers such that $f(0) = 0$ , $f(6) = 12$ , and

|x - y| \leqslant |f(x) - f(y)| \leqslant 3|x - y| \quad \text{for all } x, y \in A.

Find the number of such functions $f$ .

Answer

Solution

Difficulty	6/10
Topics	combinatorics, functions, Counting, Casework

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