Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,…, players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on.
The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.
The following information is known about Rounds 1 through 6:
1. Gordon did not score consecutively in any two rounds.
2. Eric and Fatima both scored in a round. The following information is known about Rounds 7 through 10:
1. Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
2. Joshin scored in Round 7, while Amita scored in Round 10.
3. No player scored in all the four rounds.
Here is the data converted into a clean table format:
| Player No. | Player Name | Points after Round 6 | Points after Round 10 |
|---|---|---|---|
| 1 | Amita | 8 | 18 |
| 2 | Bala | 2 | 5 |
| 3 | Chen | 3 | 6 |
| 4 | David | 6 | 6 |
| 5 | Eric | 3 | 10 |
| 6 | Fatima | 10 | 10 |
| 7 | Gordon | 17 | 17 |
| 8 | Hansa | 1 | 4 |
| 9 | Ikea | 2 | 17 |
| 10 | Joshin | 14 | 17 |
Q. 1 What were the scores of Chen, David, and Eric respectively after Round 3?
1) 3, 3, 3 2) 3, 3, 0 3) 3, 6, 3 4) 3, 0, 3
Q. 2 Which three players were in the last three positions after Round 4?
1) Bala, Hansa, Ikea 2) Bala, Chen, Gordon 3) Bala, Ikea, Joshin 4) Hansa, Ikea, Joshin
Q. 3 Which player scored points in maximum number of rounds?
1) Chen 2) Joshin 3) Amita 4) Ikea
Q. 4 Which players scored points in the last round?
1) Amita, Bala, Chen 2) Amita, Eric, Joshin 3) Amita, Chen, Eric 4) Amita, Chen, David
🧾 Understanding the Setup:
Game Format:
- There are 10 players, numbered 1 to 10, each with a name.
- The game has 10 rounds, and each round involves 6 players.
- In each round:
- Top scorer gets 7 points
- 2nd place gets 3 points
- 3rd place gets 1 point
- No ties in rankings.
- Each round involves a rotating group of 6 players (moving window):
- R1: Players 1–6
- R2: Players 2–7
- …
- R6: Players 6–10, 1
- R7: Players 7–10, 1–2
- R8: Players 8–10, 1–3
- R9: Players 9–10, 1–4
- R10: Players 10, 1–5
🧾 Score Table Summary:
| Player | Score after R6 | Score after R10 | Gain (R7–R10) |
|---|---|---|---|
| Amita | 8 | 18 | 10 |
| Bala | 2 | 5 | 3 |
| Chen | 3 | 6 | 3 |
| David | 6 | 6 | 0 |
| Eric | 3 | 10 | 7 |
| Fatima | 10 | 10 | 0 |
| Gordon | 17 | 17 | 0 |
| Hansa | 1 | 4 | 3 |
| Ikea | 2 | 17 | 15 |
| Joshin | 14 | 17 | 3 |
⚙️ Logic Used from Clues:
From Rounds 1–6:
- Clue: Gordon did not score in two consecutive rounds
- Clue: Eric and Fatima scored in the same round
From Rounds 7–10:
- Only two players scored in three consecutive rounds → One is Chen
- No other player scored in two consecutive rounds
- Joshin scored in Round 7
- Amita scored in Round 10
- No one scored in all four of R7–R10
These constraints allowed the final solution grid (as in your image) to be completed.
✅ Now, Let’s Answer the Questions:
### Q.1 What were the scores of Chen, David, and Eric respectively after Round 3?
From solution grid:
- Chen scored in Round 2: 3 points
- David scored in Round 1 and 2: 3 + 3 = 6
- Eric scored in Round 3: 3 points
➡️ After Round 3:
- Chen = 3
- David = 6
- Eric = 3
✅ Answer: 3) 3, 6, 3
### Q.2 Which three players were in the last three positions after Round 4?
From grid tracking up to Round 4:
| Player | Score after R4 |
|---|---|
| Hansa | 0 |
| Ikea | 0 |
| Joshin | 0 |
They all scored later (in R5 or after), but had 0 after R4.
✅ Answer: 4) Hansa, Ikea, Joshin
### Q.3 Which player scored points in maximum number of rounds?
Track per-player round-wise score distribution (from final grid):
- Joshin scored in: R5, R6, R7, R8, R10 → 5 rounds
- Chen scored in: R2, R3, R7, R8 → 4 rounds
- Amita: R1, R5, R10 → 3 rounds
- Ikea: R7, R8, R9, R10 → 4 rounds
Hence:
✅ Joshin scored in maximum rounds (5)
✅ Answer: 4) Joshin
### Q.4 Which players scored in the last round (Round 10)?
From Round 10 participant list (Players 10, 1, 2, 3, 4, 5):
Players:
- Joshin
- Amita
- Bala
- Chen
- David
- Eric
From final grid, Round 10 scorers were:
- Amita → 7
- Chen → 3
- Eric → 1
✅ Answer: 3) Amita, Chen, Eric
