Some positive integers, sum of which is $23$, are written in sequential form. Neither one of the terms nor the sum of some consecutive terms in the sequence is equal to $3$. a) Is it possible that the sequence contains exactly $11$ terms? b)Is it possible that the sequence contains exactly $12$ terms?
Problem
Source: Kosovo MO 2020 Grade 11, Problem 1
Tags: Sequence, terms, national olympiad, Olympiad, Kosovo, algebra, combinatorics