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Partition of a set

Source: Turkey JBMO Team Selection Test Problem 2

May 29, 2012
inductionfloor functionlogarithmscombinatorics proposedcombinatorics

Problem Statement

Let S={1,2,3,…,2012}.S=\{1,2,3,\ldots,2012\}. We want to partition SS into two disjoint sets such that both sets do not contain two different numbers whose sum is a power of 2.2. Find the number of such partitions.
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