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 $3$?
- $3,3,3$
- $3,0,3$
- $3,6,3$
- $3,3,0$