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Problem of the Week
Problem D
Take a Seat 2

Twelve people are seated, equally spaced, around a circular table. They each hold a card with different integer 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 holding the integers \(3\), \(4\), and \(8\) are seated as shown. The person opposite the person holding \(8\) is holding the integer \(x\). What are the possible values of \(x\)?

Twelve chairs are evenly spaced around a circle. Starting at the chair labelled 4 and moving clockwise around the circle, there is a chair with no label, then a chair labelled 8, then two chairs with no labels, then a chair labelled 3, then two chairs with no labels, then a chair labelled x, then three chairs with no labels, before arriving back at the chair labelled 4.