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Difference of digits one

Source: IMOTC 2015 Practice Test 1 Problem 2

July 11, 2015
combinatorics

Problem Statement

A 1010-digit number is called a <spanclass=′latex−italic′>cute</span><span class='latex-italic'>cute</span> number if its digits belong to the set {1,2,3}\{1,2,3\} and the difference of every pair of consecutive digits is 11. a) Find the total number of cute numbers. b) Prove that the sum of all cute numbers is divisibel by 14081408.
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