Question 69
A 10 digit positive integer is called a *cute number* if its digits are from the set $\{1, 2, 3\}$ and every two consecutive digits differ by 1.
a) Prove that exactly 5 digits of a cute number are equal to 2.
b) Find the total number of cute numbers.
c) Prove that the sum of all cute numbers is divisible by 1408.
a) Prove that exactly 5 digits of a cute number are equal to 2.
b) Find the total number of cute numbers.
c) Prove that the sum of all cute numbers is divisible by 1408.