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Team A and Team B have entered a chess competition - HSC - SSCE Mathematics Standard - Question 9 - 2020 - Paper 1
Question 9
Team A and Team B have entered a chess competition. Team A and Team B have three members each. Each member of Team A must play each member of Team B once. Which of... show full transcript
Worked Solution & Example Answer:Team A and Team B have entered a chess competition - HSC - SSCE Mathematics Standard - Question 9 - 2020 - Paper 1
Step 1
Which of the following network diagrams could represent the chess games to be played?
Answer
To determine the correct network diagram for the chess games, we must understand that each member of Team A, comprising 3 members, plays a game against each member of Team B, which also has 3 members. Thus each member in Team A will play 3 games, leading to a total of 3 x 3 = 9 games.
Next, we analyze each option:
- Option A displays a hexagon, which implies a different number of total connections, thus it cannot represent the total games played.
- Option B shows a triangular arrangement where each vertex connects adequately with the others. This option allows for 9 total connections, fitting our requirement.
- Option C resembles Option A but with more vertices, again failing to meet our total connections criteria.
- Option D displays a configuration with fewer total connections than required.
Therefore, the only suitable representation of the chess matches played is Option B.