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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 $2,\dots,$ 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 $10$.

 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 $14$ $17$

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.

Which players scored points in the last round?

1. Amita, Chen, Eric
2. Amita, Chen, David
3. Amita, Bala, Chen
4. Amita, Eric, Joshin

1 vote