Problem

Source: Turkey JBMO Team Selection Test Problem 2

Tags: induction, floor function, logarithms, combinatorics proposed, combinatorics



Let $S=\{1,2,3,\ldots,2012\}.$ We want to partition $S$ into two disjoint sets such that both sets do not contain two different numbers whose sum is a power of $2.$ Find the number of such partitions.