# Cute numbers!

**Discrete Mathematics**Level 5

Define a *cute* number as a 16 digit number whose difference in pair of each consecutive digits is \(1\) and each digit belongs to the set \( \{ 1,2,3 \} \).

If the the sum of all *cute* numbers can be expressed as \(2^{a} \times b \) where \( b\) is not divisible by \(2\), and both \(a\) and \(b\) are positive integers.Evaluate \(a+b\).