MathDB
Find the greatest possible number of symbols

Source: Ukrainian TST 2008 Problem 2

February 12, 2009
inequalitiescombinatorics unsolvedcombinatoricsalgebra

Problem Statement

There is a row that consists of digits from 0 0 to 9 9 and Ukrainian letters (there are 33 33 of them) with following properties: there aren’t two distinct digits or letters ai a_i, aj a_j such that ai>aj a_i > a_j and i<j i < j (if ai a_i, aj a_j are letters ai>aj a_i > a_j means that ai a_i has greater then aj a_j position in alphabet) and there aren’t two equal consecutive symbols or two equal symbols having exactly one symbol between them. Find the greatest possible number of symbols in such row.