Problem

Source: IMOTC 2015 Practice Test 1 Problem 2

Tags: combinatorics



A $10$-digit number is called a $\textit{cute}$ number if its digits belong to the set $\{1,2,3\}$ and the difference of every pair of consecutive digits is $1$. a) Find the total number of cute numbers. b) Prove that the sum of all cute numbers is divisibel by $1408$.