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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.

What were the scores of Chen, David, and Eric respectively after Round $3$?

1. $3,3,3$
2. $3,0,3$
3. $3,6,3$
4. $3,3,0$

1 vote