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The maximal number of terms that could remain on their place

Source: Tournament of Towns Spring 2003 - Senior O-Level - Problem 4

June 14, 2011
number theory proposednumber theory

Problem Statement

In the sequence 00,01,02,03,,9900, 01, 02, 03,\ldots , 99 the terms are rearranged so that each term is obtained from the previous one by increasing or decreasing one of its digits by 11 (for example, 2929 can be followed by 19,3919, 39, or 2828, but not by 3030 or 2020). What is the maximal number of terms that could remain on their places?