Achievable Absolute Sums

★ 7/10combinatorics Absolute Value algebra sequences Induction Telescoping

Problem

A sequence $A \colon a_0, a_1, a_2, \dots, a_{20}$ satisfies $a_0 = 0$ and

|a_i| = |a_{i-1} + 1|, \qquad i = 1, 2, \dots, 20.

For each of the values $0$ , $2$ , $10$ , $12$ , determine whether there exists such a sequence with

\left|a_0 + a_1 + a_2 + \cdots + a_{20}\right|

equal to that value.

Answer

Solution

Difficulty	7/10
Topics	combinatorics, Absolute Value, algebra, sequences, Induction, Telescoping

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