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UKMT Junior Kangaroo, 2021

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows the eight vertices of an octagon connected by line segments. Jodhvir wants to write one of the integers 1, 2, 3 or 4 at each of the vertices so that the two integers at the ends of every line segment are different. He has already written three integers as shown. How many times will the integer 4 appear in his completed diagram?

(A) $5$ (B) $4$ (C) $3$ (D) $2$ (E) $1$

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