Six teams are playing in a hockey tournament where each team is playing against every other team exactly once. At an intermediate stage, the status is as follows:
Notes:
• The team that scores more goals than it concedes wins the match, while if both the teams score the same no. of goals, the match is declared drawn.
• Ina match played between Team X and Team Y, if team X scores 1 and concedes none. then the score line would read: Team X — Team Y (1-0)
Solution
Team A has won both its matches and scored 5 goals while conceding 1. Thus, the possible scorelines for team A are (4-1) & (1-0), (3-1) & (2-0), (2-1) & (3-0).
Similarly, the possible outcomes for others teams are as follows:
B: (5-1) & (0-0) and (4-0) & (1-1)
C: (2-0) & (0-0) and (1-0) & (1-1)
D: (0-0) & (1-1)
E: (0-2) & (1-2) and (0-1) & (1-3)
F: (0-1) & (0-6), (0-2) & (0-5) and so on.
By carefully observing the above scorelines, the following table can be obtained.
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From the above table, we can see that options B, C and D are possible and option A is not.
Hence, option A is the answer.
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