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The greatest n

Source: Bulgarian MO 2007, Day 1, Problem 2

May 16, 2007
combinatorics proposedcombinatoricsBulgaria

Problem Statement

Find the greatest positive integer nn such that we can choose 20072007 different positive integers from [2⋅10n−1,10n)[2\cdot 10^{n-1},10^{n}) such that for each two 1≤i<j≤n1\leq i<j\leq n there exists a positive integer a1a2…an‾\overline{a_{1}a_{2}\ldots a_{n}} from the chosen integers for which aj≥ai+2a_{j}\geq a_{i}+2.
A. Ivanov, E. Kolev
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