MathDB
Consecutive numeral block hunting

Source: 2023 Turkey MO 2nd Round P3

December 21, 2023
combinatorics

Problem Statement

Let a 99-digit number be balanced if it has all numerals 11 to 99. Let SS be the sequence of the numerals which is constructed by writing all balanced numbers in increasing order consecutively. Find the least possible value of kk such that any two subsequences of SS which has consecutive kk numerals are different from each other.