Problem C

Take a Seat 1

Twelve people are seated around a circular table. They each hold a card with a different integer from \(1\) to \(12\) on it. For any two people sitting beside each other, the positive difference between the integers on their cards is no more than \(2\). The people with integers \(1\), \(3\), \(a\), and \(b\) are seated as shown.

What is the value of \(a + b\)?

Note: The *positive difference*
between two numbers is found by subtracting the smaller number from the
larger number.

**Theme: **Computational Thinking