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Problem of the Week
Problem D
Not as Easy as 1, 2, 3

Zephaniah places the numbers \(1\), \(2\), and \(3\) in the circles below so that each circle contains exactly one of \(1\), \(2\), and \(3\), and any two circles joined by a line do not contain the same number. He then finds the sum of the numbers in the four circles on the far right. What sums could he achieve?

Seven circles are arranged into three vertical columns with lines connecting some pairs of circles. There is one circle in the left column, two circles in the middle column, and four circles in the right column. The left circle is connected to each of the two middle circles. The two middle circles are connected to each other. The top middle circle is connected to the top two circles on the right. The top two circles on the right are connected. The bottom middle circle is connected to the bottom two circles on the right. The bottom two circles on the right are connected.