Show that the set $\{1,2,....,2^n\}$ can be partitioned in two classes, none of which contains an arithmetic progression of length $2n$.
Problem
Source: Romania BMO TST 1993 p3
Tags: arithmetic sequence, partition, Subsets, combinatorics
Source: Romania BMO TST 1993 p3
Tags: arithmetic sequence, partition, Subsets, combinatorics
Show that the set $\{1,2,....,2^n\}$ can be partitioned in two classes, none of which contains an arithmetic progression of length $2n$.