Six football teams — Panthers, Quakers, Raptors, Strikers, Titans and Unity — played a single round-robin tournament: each team played every other team exactly once (15 matches in total). A win earns a team 3 points, a draw earns each team 1 point, and a loss earns 0 points. There were no goals data; only the match outcome (win/draw/loss) matters.
The results of 12 of the 15 matches are known directly:
- Panthers beat Quakers, Panthers beat Raptors, Panthers drew with Strikers, Panthers beat Titans, Panthers beat Unity.
- Quakers beat Raptors, Quakers drew with Strikers.
- Raptors lost to Strikers, Raptors drew with Titans, Raptors beat Unity.
- Strikers beat Titans, Strikers beat Unity.
The results of the Quakers-Titans, Quakers-Unity and Titans-Unity matches are not stated directly. However, the final Won-Drawn-Lost-Points record of every team (after all 15 matches) is known and is given below.
| Team | Won | Drawn | Lost | Points |
|---|---|---|---|---|
| Panthers | 4 | 1 | 0 | 13 |
| Quakers | 2 | 1 | 2 | 7 |
| Raptors | 1 | 1 | 3 | 4 |
| Strikers | 3 | 2 | 0 | 11 |
| Titans | 1 | 2 | 2 | 5 |
| Unity | 0 | 1 | 4 | 1 |
Use the known results together with each team's final Won-Drawn-Lost record to work out the outcomes of the three unstated matches.
The results of 12 of the 15 matches are known directly:
- Panthers beat Quakers, Panthers beat Raptors, Panthers drew with Strikers, Panthers beat Titans, Panthers beat Unity.
- Quakers beat Raptors, Quakers drew with Strikers.
- Raptors lost to Strikers, Raptors drew with Titans, Raptors beat Unity.
- Strikers beat Titans, Strikers beat Unity.
The results of the Quakers-Titans, Quakers-Unity and Titans-Unity matches are not stated directly. However, the final Won-Drawn-Lost-Points record of every team (after all 15 matches) is known and is given below.
| Team | Won | Drawn | Lost | Points |
|---|---|---|---|---|
| Panthers | 4 | 1 | 0 | 13 |
| Quakers | 2 | 1 | 2 | 7 |
| Raptors | 1 | 1 | 3 | 4 |
| Strikers | 3 | 2 | 0 | 11 |
| Titans | 1 | 2 | 2 | 5 |
| Unity | 0 | 1 | 4 | 1 |
Use the known results together with each team's final Won-Drawn-Lost record to work out the outcomes of the three unstated matches.
Question 1
Single correct option
Which team won the tournament (i.e., finished with the most points)?
- A. Panthers
- B. Strikers
- C. Quakers
- D. Titans
Show answer and solution
Answer: (A) Panthers
Reading the given final points column directly, Panthers has 13 points, the highest of all six teams (Strikers is next with 11).
Question 2
Single correct option
What was the result of the match between Quakers and Titans?
- A. Quakers won
- B. Titans won
- C. It was a draw
- D. Cannot be determined
Show answer and solution
Answer: (B) Titans won
From the 12 known results, Quakers already has 2 wins (vs Raptors, and one more needed to total 2 — actually Quakers' only known win is vs Raptors) and 1 draw (vs Strikers) and 1 loss so far is unaccounted; Quakers' final record is 2W-1D-2L. Its known matches (vs Panthers: L, vs Raptors: W, vs Strikers: D) give 1W-1D-1L, leaving 1W-0D-1L still needed from its two unknown matches (vs Titans, vs Unity). Similarly Titans' known matches (vs Panthers: L, vs Raptors: D, vs Strikers: L) give 0W-1D-2L against a final record of 1W-2D-2L, leaving 1W-1D-0L needed from its two unknown matches (vs Quakers, vs Unity). Since Titans needs exactly one more win and one more draw from its two remaining matches, and Quakers needs one win and one loss from its two remaining matches, testing the combination shows Titans must beat Quakers (satisfying Quakers' needed loss and part of Titans' needed win) and Titans must draw with Unity (satisfying Titans' needed draw), which forces Quakers to beat Unity for Quakers' needed win. This is the only consistent assignment.
Question 3
Single correct option
What was the result of the match between Quakers and Unity?
- A. Quakers won
- B. Unity won
- C. It was a draw
- D. Cannot be determined
Show answer and solution
Answer: (A) Quakers won
As established, Quakers needed one win and one loss from its two unknown matches (vs Titans, vs Unity), and Titans beating Quakers accounts for the loss, so Quakers must have beaten Unity to complete its record of 2W-1D-2L.
Question 4
Single correct option
What was the result of the match between Titans and Unity?
- A. Titans won
- B. Unity won
- C. It was a draw
- D. Cannot be determined
Show answer and solution
Answer: (C) It was a draw
Titans needed exactly one more win and one more draw from its two unknown matches (vs Quakers, vs Unity). Since Titans beat Quakers (the win), the Titans-Unity match must be the draw, consistent with Titans' final record of 1W-2D-2L.
Question 5
Numerical answer
How many of the 15 matches in the tournament ended in a draw?
Show answer and solution
Answer: 4
Known draws: Panthers-Strikers, Quakers-Strikers, Raptors-Titans, and (from the deduction above) Titans-Unity — a total of 4 draws. This is also consistent with the Drawn column of the table: total drawn-team-appearances = 1+1+1+2+2+1 = 8, and since each draw is counted for two teams, number of drawn matches = 8/2 = 4.
Question 6
Numerical answer
Find the difference in points between the tournament winner and the last-placed team.
Show answer and solution
Answer: 12
The winner, Panthers, has 13 points. The last-placed team, Unity, has 1 point. Difference = 13 − 1 = 12.
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