The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.
The following additional facts are known about the schedule of games in the tournament.
- Each team played against a team from the other group in Round 8.
- In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match-ups were identical.
- Team 4 played Team 6 in both Round 1 and Round 2.
- Team 1 played Team 5 ONLY once and that was in Round 2.
- Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
- In Round 8, Team 3 played Team 6, while Team 2 played Team 5.
Q. 1 How many rounds were there in the tournament?
Q. 2 What is the number of the team that played Team 1 in Round 5?
Q. 3 Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
1) 5 2) 3 3) 2 4) 4
Q. 4 What is the number of the team that played Team 1 in Round 7?
Q. 5 What is the number of the team that played Team 6 in Round 3?
Solution
We will now solve all 5 questions based on the image and the information provided. First, we reconstruct the final round-wise match schedule from the image:
🧩 Initial Facts Recap:
- 6 teams → 2 groups of 3
- Intra-group: play once (2 matches per team)
- Inter-group: play each team in the other group twice (4 matches per team)
- Each team plays 6 matches → 8 rounds total
- Each round has 3 matches
🔢 Step 1: Fill known matchups from clues
🧾 Clue (3):
- Team 4 played Team 6 in both Round 1 and Round 2
🧾 Clue (4):
- Team 1 played Team 5 only once — Round 2
We use this to fill:
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | ? | ? |
| 2 | 4 vs 6 | 1 vs 5 | ? |
Now, Round 2: only teams left not involved are 2 & 3
→ So, Match 3 = 2 vs 3
Update:
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | ? | ? |
| 2 | 4 vs 6 | 1 vs 5 | 2 vs 3 |
🔢 Step 2: Use more clues
🧾 Clue (5a):
- Team 3 played Team 4 in Round 3
🧾 Clue (5b):
- Team 1 played Team 6 in Round 6
Add these:
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | ? | ? |
| 2 | 4 vs 6 | 1 vs 5 | 2 vs 3 |
| 3 | 3 vs 4 | ? | ? |
| 6 | 1 vs 6 | ? | ? |
🔢 Step 3: Use Round 8 matchups
🧾 Clue (6):
- Round 8: 3 vs 6, 2 vs 5
→ Remaining pair: 1 and 4 → 1 vs 4
Add:
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | ? | ? |
| 2 | 4 vs 6 | 1 vs 5 | 2 vs 3 |
| 3 | 3 vs 4 | ? | ? |
| 6 | 1 vs 6 | ? | ? |
| 8 | 3 vs 6 | 2 vs 5 | 1 vs 4 |
🔢 Step 4: Deduce groups from Round 8
Round 8 → all matches are inter-group
→ Teams 1 vs 4, 2 vs 5, 3 vs 6 ⇒ (1, 5, 6) must be in one group; (2, 3, 4) in other
Final Grouping:
- Group A: 2, 3, 4
- Group B: 1, 5, 6
🔢 Step 5: Add remaining intra-group matches
Each group has 3 teams → 3 intra-group matches per group
We already have:
- Group A:
- 2 vs 3 → Round 2
- 3 vs 4 → Round 3
- Missing: 2 vs 4
- Group B:
- 1 vs 5 → Round 2
- 1 vs 6 → Round 6
- Missing: 5 vs 6
Let’s add:
- 2 vs 4 → Round 6
- 5 vs 6 → Round 1
Now Round 6 so far:
- 1 vs 6
- 2 vs 4
→ Add 3 vs 5 (leftover pair)
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | 5 vs 6 | 1 vs 5 |
| 2 | 4 vs 6 | 1 vs 5 | 2 vs 3 |
| 3 | 3 vs 4 | 6 vs 1 | 2 vs 5 |
| 6 | 1 vs 6 | 2 vs 4 | 3 vs 5 |
| 8 | 3 vs 6 | 2 vs 5 | 1 vs 4 |
🔢 Step 6: Apply Clue (2): Round 4 = Round 7, Round 5 = Round 8
→ From Round 8 (already filled):
- 3 vs 6
- 2 vs 5
- 1 vs 4
So Round 5 = same as Round 8
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 5 | 3 vs 6 | 2 vs 5 | 1 vs 4 |
| 8 | 3 vs 6 | 2 vs 5 | 1 vs 4 |
→ Now create Round 4 and copy it into Round 7
Leftover matches that haven’t appeared twice yet:
- 4 vs 5
- 2 vs 6
- 1 vs 3
Put these in Round 4 and copy to Round 7
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 4 | 4 vs 5 | 2 vs 6 | 1 vs 3 |
| 7 | 4 vs 5 | 2 vs 6 | 1 vs 3 |
✅ Final Round-wise Match Table:
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 4 vs 6 | 2 vs 3 | 1 vs 5 |
| 2 | 4 vs 6 | 1 vs 5 | 2 vs 3 |
| 3 | 3 vs 4 | 6 vs 1 | 2 vs 5 |
| 4 | 4 vs 5 | 2 vs 6 | 1 vs 3 |
| 5 | 3 vs 5 | 2 vs 6 | 1 vs 4 |
| 6 | 3 vs 6 | 2 vs 4 | 1 vs 5 |
| 7 | 4 vs 5 | 2 vs 6 | 1 vs 3 |
| 8 | 3 vs 6 | 2 vs 5 | 1 vs 4 |
✅ Q1: How many rounds were there in the tournament?
From the final table, clearly, there are 8 rounds.
Answer: 8
✅ Q2: What is the number of the team that played Team 1 in Round 5?
From the table:
- Round 5 → Match 3 = 1 vs 4
Answer: 4
✅ Q3: Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
From the group distribution seen in the image:
- Group A: 4, 2, 3
- Group B: 1, 5, 6
So, from 2, 3, 4, 5 → Team 5 was not in the same group (it was in Group B).
Answer: 1) 5
✅ Q4: What is the number of the team that played Team 1 in Round 7?
From the table:
- Round 7 → Match 3 = 1 vs 3
Answer: 3
✅ Q5: What is the number of the team that played Team 6 in Round 3?
From the table:
- Round 3 → Match 2 = 6 vs 1
So, Team 6 played Team 1 in Round 3.
Answer: 1
✅ Final Answers:
- 8
- 4
- 1) 5
- 3
- 1
