CEMC Banner

Problem of the Week
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 \(a + b\)?

Twelve chairs are evenly spaced around a circle. Starting at the chair labelled 3 and moving counterclockwise around the circle, there is a chair labelled 1, then three chairs with no labels, then a chair labelled a, then a chair with no label, then a chair labelled b, then four chairs with no labels, before arriving back at the chair labelled 3.

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

Theme: Computational Thinking