P looks at Q while Q looks at R. P is married. R is not married. The number of pairs of people in which a married person...

Question

P looks at Q while Q looks at R. P is married. R is not married. The number of pairs of people in which a married person is looking at an unmarried person is:

A. 0
B. 1
C. 2
D. Cannot be determined

Accepted Answer

B. 1 We have a chain P -> Q -> R. P is married, R is unmarried, and Q's marital status is unknown. We count pairs (X, Y) where X is married, X looks at Y, and Y is unmarried. P looks at Q and Q looks at R are the only two looking-at relationships. We handle both cases for Q. If Q is married: P (married) looks at Q (married) — no. Q (married) looks at R (unmarried) — yes! Count = 1. If Q is unmarried: P (married) looks at Q (unmarried) — yes! Q (unmarried) looks at R (unmarried) — no (Q is not married). Count = 1. In both cases the answer is exactly 1.

P looks at Q while Q looks at R. P is married. R is not married. The number of pairs of people in which a married person is looking at an unmarried person is: A. 0 B. 1 C. 2 D. Cannot be determined