MathDB
transform 21062011 into 1012011 by 3 operations

Source: JBMO 2011 Shortlist C3

October 14, 2017
JBMOcombinatorics

Problem Statement

We can change a natural number nn in three ways: a) If the number nn has at least two digits, we erase the last digit and we subtract that digit from the remaining number (for example, from 123123 we get 12āˆ’3=912 - 3 = 9); b) If the last digit is different from 00, we can change the order of the digits in the opposite one (for example, from 123123 we get 321321); c) We can multiply the number nn by a number from the set {1,2,3,...,2010} \{1, 2, 3,..., 2010\}. Can we get the number 2106201121062011 from the number 10120111012011?