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.
From the given information, we can see that each player participated in only a certain number of rounds. The following table provides the rounds that each person participated in (split by Rounds 1 - 6 and Rounds 7 - 10):
Person | Rounds participated From 1 to 6 | Rounds participated From 7 to 10 |
Amita | 1, 6 | 7, 8, 9, 10 |
Bala | 1, 2 | 7, 8, 9, 10 |
Chen | 1, 2, 3 | 8, 9, 10 |
David | 1,2, 3,4 | 9, 10 |
Eric | 1,2, 3, 4,5 | 10 |
Fatima | 1,2, 3, 4, 5,6 | - |
Gordon | 2, 3, 4, 5, 6 | 7 |
Hansa | 3, 4, 5, 6 | 7,8 |
Ikea | 4, 5,6 | 7, 8, 9 |
Joshin | 5, 6 | 7, 8, 9, 10 |
Rounds 1 to 6:
The points that Amita scored till Round 6 is 8. Among the rounds 1 to 6. he participated only in Round 1 and Round 6. Hence, he must have scored 7 and 1 points in Round 1 and Round 6 in any order.
Since Bala scored 2 points till Round 6, he must have scored 1 point in Round 1 and 1 point in Round 2.
Since Bala scored 1 point in Round 1. Amita could not have scored 1 point in Round 1. Hence. Amita must have scored 7 points in Round 1 and 1 point in Round 6.
Gordon scored 17 points in Rounds 2 to 6. It is given that from Round 1 to Round 6. Gordon did not score consecutively in any two rounds. Since it is not possible to score 17 points in two rounds. Gordon must have scored 17 points in three rounds - Round 2, Round 4 and Round 6.
In these three rounds, he must have scored 7, 7 and 3 points, in any order.
Joshin scored 14 points in Rounds 5 and 6. Hence, he must have scored 7 points in each of these two rounds. Since Joshin scored 7 points in Round 6, Gordon cannot score 7 points in Round 6. Hence, Gordon must have scored 3 points in Round 6 and 7 points in each of Round 2 and Round 4.
Ikea scored 2 points till Round 6. In the first 6 rounds, he played in only Rounds 4. 5 and 6, of which he scored 0 points in Round 6. Hence, he must have scored 1 point each in Round 4 and Round 5.
Hansa scored 1 point in the first 6 rounds. He played in only Rounds 3 to 6. Of these rounds, he did not score any point in Round 6. In Rounds 4 and 5. Ikea scored 1 point. Hence. Hansa could not have scored 1 point in Rounds 4 and 5.
Therefore, Hansa must have scored 1 point in Round 3.
Eric scored 3 points in the first 6 rounds. He could have scored 1 point in each of three rounds OR 3 points in one round. He participated only in Rounds 1 to 5. Of these rounds, Bala scored 1 point each in Round 1 and 2. Hansa scored 1 point in Round 3, while Ikea scored 1 point in Round 4 and Round 5. Hence. Eric could not have scored 1 point each in three rounds. Hence. Eric must have scored 3 points in one round.
Similarly. Fatima cannot score 7. 1. 1, 1 point in four rounds (among the first 6 rounds) and must have scored 7 points and 3 points in two rounds.
Given that Eric and Fatima both scored in one round. In the round that both of them scored. Eric must have scored 3 points, while Fatima must have score 7 points (since both of them cannot score the same number of points in a round).
Among the rounds that both Eric and Fatima played (i.e.. Rounds 1 to 5), the only round in which Fatima could have scored 7 points is Round 3. Hence, in round 3. Fatima must have scored 7 points and Eric must have scored 3 points. Eric should have scored 0 in all the other rounds from rounds 1 to 6.
Chen must have scored 3 points in one of the rounds, while David must have scored 3 points in two rounds each. Irrespective of which round Chen scored 3 points, David must have scored 3 points in Round 4. In the first two rounds, Chen and David must have scored 3 points in any order. Hence, Fatima could have scored 3 points only in Round 5.
Rounds 7 to 10:
In rounds 7-10, Chen must have scored 3 points (since he scored 6 points in total, after Round 10). Since Chen played 3 rounds from 7-10 and he scored in three consecutive rounds among these rounds, he must have scored 1 point each in Round 8, Round 9 and Round 10.
Ikea scored 15 points in Rounds 7 to 10. Since he played only in Rounds 7, 8 and 9. he must have scored 7, 7 and 1 points in these three rounds, in any order. Since Chen scored 1 point each in Rounds 8 and 9. Ikea could have
scored 1 point only in Round 7. In Rounds 8 and 9, he must have scored 7 points each.
Joshin scored 3 points in Rounds 7 to 10. He could not have scored 1 point in each of three rounds (since Ikea and Chen are the only persons who scored in three consecutive rounds and no one else scored in any two consecutive rounds).
Hence, Joshin must have scored 3 points in one round. Since it is given that Joshin scored in Round 7, he must
have scored 3 points in Round 7 and no points in the other rounds.
In Round 7, Ikea scored 1 point and Joshin scored 3 points. The only person who could have scored 7 points in Round 7 is Amita.
Hansa would have scored 3 points in Round 8 (since he scored 0 in Round 7).
Eric scored 7 points in Rounds 7 to 10. Among the rounds that he played (Rounds 9, 10), he must have scored 7 points in Round 10 (since Ikea scored 7 points in Round 9).
David did not score any points in Rounds 7 through 10.
Amita must have scored 3 points in Round 10 (since Amita scored in Round 10) and Bala must have scored 3 points in Round 9.
The table below provides the points scored by all the players in all the rounds. An X' indicates that the player did not participate in that round.
| A | B | C | D | E | F | G | H | 1 | J |
1 | 7 | 1 | 3/0 | 0/3 | 0 | 0 | X | X | X | X |
2 | X | 1 | 0/3 | 3/0 | 0 | 0 | 7 | X | X | X |
3 | X | X | 0 | 0 | 3 | 7 | 0 | 1 | X | X |
4 | X | X | X | 3 | 0 | 0 | 7 | 0 | 1 | X |
5 | X | X | X | X | 0 | 3 | 0 | 0 | 1 | 7 |
6 | 1 | X | X | X | X | 0 | 3 | 0 | 0 | 7 |
7 | 7 | 0 | X | X | X | X | 0 | 0 | 1 | 3 |
8 | 0 | 0 | 1 | X | X | X | X | 3 | 7 | 0 |
9 | 0 | 3 | 1 | 0 | X | X | X | X | 7 | 0 |
10 | 3 | 0 | 1 | 0 | 7 | X | X | X | X | 0 |
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