Five snooker players — A, B, C, D and E — play a round-robin tournament in which every player plays every other player exactly once (10 matches in total). Each match is played as a "best-of-5" contest: the first player to win 3 frames wins the match, so every match score is one of 3–0, 3–1 or 3–2. A player earns 2 points for winning a match and 0 points for losing (there are no draws). The frame scores of all 10 matches are given below.
| Match | Score |
|---|---|
| A vs B | A won 3–1 |
| A vs C | A won 3–0 |
| A vs D | D won 3–2 |
| A vs E | A won 3–2 |
| B vs C | C won 3–1 |
| B vs D | B won 3–0 |
| B vs E | E won 3–1 |
| C vs D | C won 3–2 |
| C vs E | E won 3–0 |
| D vs E | D won 3–1 |
Whenever two or more players finish with equal points, they are ranked by frame difference (frames won minus frames lost across all their matches), with a higher frame difference ranked above a lower one.
| Match | Score |
|---|---|
| A vs B | A won 3–1 |
| A vs C | A won 3–0 |
| A vs D | D won 3–2 |
| A vs E | A won 3–2 |
| B vs C | C won 3–1 |
| B vs D | B won 3–0 |
| B vs E | E won 3–1 |
| C vs D | C won 3–2 |
| C vs E | E won 3–0 |
| D vs E | D won 3–1 |
Whenever two or more players finish with equal points, they are ranked by frame difference (frames won minus frames lost across all their matches), with a higher frame difference ranked above a lower one.
Question 1
Single correct option
Which player won the most frames in total across the tournament?
- A. A
- B. D
- C. C
- D. E
Show answer and solution
Answer: (A) A
Tallying frames won by each player from the ten scores: A (vs B:3, vs C:3, vs D:2, vs E:3) = 11; B (vs A:1, vs C:1, vs D:3, vs E:1) = 6; C (vs A:0, vs B:3, vs D:3, vs E:0) = 6; D (vs A:3, vs B:0, vs C:2, vs E:3) = 8; E (vs A:2, vs B:3, vs C:3, vs D:1) = 9. The highest total is A, with 11 frames won.
Question 2
Numerical answer
What is player C's overall frame difference (frames won minus frames lost)?
Show answer and solution
Answer: -3
C's matches: vs A lost 0–3, vs B won 3–1, vs D won 3–2, vs E lost 0–3. Frames won = 0+3+3+0 = 6. Frames lost = 3+1+2+3 = 9. Frame difference = 6 − 9 = −3.
Question 3
Single correct option
Using 2 points per match win (ties broken by frame difference), who finishes 2nd in the final standings?
- A. B
- B. C
- C. D
- D. E
Show answer and solution
Answer: (D) E
Points (2 per win): A=6 (3 wins), B=2 (1 win), C=4 (2 wins), D=4 (2 wins), E=4 (2 wins). Among the three tied at 4 points, frame differences (frames won − lost) are: C = 6−9 = −3; D = 8−9 = −1 (D's frames: won 3–2 vs A, lost 0–3 vs B, lost 2–3 vs C, won 3–1 vs E, giving 8 won, 9 lost); E = 9−7 = +2 (E's frames: lost 2–3 vs A, won 3–1 vs B, won 3–0 vs C, lost 1–3 vs D, giving 9 won, 7 lost). Ranking the tied trio by frame difference: E(+2) > D(−1) > C(−3). So the final order is A(1st), E(2nd), D(3rd), C(4th), B(5th) — E finishes 2nd.
Question 4
Single correct option
What was the total number of frames played across all 10 matches?
- A. 36
- B. 38
- C. 40
- D. 42
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Answer: (C) 40
Summing frames played in each match: (3+1)+(3+0)+(2+3)+(3+2)+(1+3)+(3+0)+(1+3)+(3+2)+(0+3)+(3+1) = 4+3+5+5+4+3+4+5+3+4 = 40.
Question 5
Single correct option
Which player finished with the fewest points in the tournament?
- A. B
- B. C
- C. D
- D. E
Show answer and solution
Answer: (A) B
Points earned: A=6, B=2, C=4, D=4, E=4 (2 points per match win). B won only 1 of 4 matches (beat D 3–0), earning just 2 points — the lowest of all players.
Question 6
Numerical answer
In how many of the 10 matches did the losing player win exactly 2 frames (i.e., the match ended 3–2)?
Show answer and solution
Answer: 3
Scanning the scores: A vs D (3–2), A vs E (3–2), and C vs D (3–2) are the only matches with a 3–2 scoreline. All other matches ended 3–0 or 3–1. So 3 matches ended 3–2.
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