In a football match, Rangers beat Rovers 5 – 4. The only time Rangers were ahead was after they scored the final goal. How many possible half-time scores were there?
A. 9
B. 10
C. 15
D. 16
E. 25
D. 16
If Rangers did not score in the first half, then there were five possible half-time scores from 0 – 0 to 0 – 4. However, if Rangers scored one goal in the first half then there were four possible half-time scores from 1 – 1 to 1 – 4. Similar reasoning shows that there are three possible half-time scores if Rangers scored two goals in the first half, two possible half-time scores if Rangers scored three goals in the first half and one possible half-time score if Rangers scored four goals in the first half. It is also possible that all goals were scored in the first half and that the half-time score was 5 – 4.
So the possible number of half-time scores is 5 + 4 + 3 + 2 + 1 + 1 = 16.
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