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Bosnia and Herzegovina JBMO TST 2012 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2012

September 16, 2018
combinatoricstransformationsDigits

Problem Statement

Let abcd\overline{abcd} be 44 digit number, such that we can do transformations on it. If some two neighboring digits are different than 00, then we can decrease both digits by 11 (we can transform 98709870 to 87708770 or 97609760). If some two neighboring digits are different than 99, then we can increase both digits by 11 (we can transform 98709870 to 99809980 or 98819881). Can we transform number 12201220 to: a)a) 20122012 b)b) 20212021