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Nice example. Person A pulls on one end of the broomstick. The boomstick exerts an equal and opposite force on Person A. This is one pair of NTN 3 forces. Another pair is between Person B and the other end of the broomstick. In this case no one would say that Person A and Person B forms a NTN 3 pair (even though, as you stated, they "interact" indirectly).