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Problem of the Week
Problem E
Take a Seat 3

Twelve people are sitting, equally spaced, around a circular table. They each hold a card with a 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 \(5\) and \(6\) are seated as shown. The person opposite the person holding the \(6\) is holding the integer \(x\). What are the possible values of \(x\)?

Twelve chairs are evenly spaced around a circle. The two
chairs labelled 5 and 6 are side by side. The chair opposite 6 is
labelled x.