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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 three players were in the last three positions after Round $4$?

  1. Bala, Chen, Gordon 
  2. Bala, Hansa, lkea
  3. Bala, Ikea, Joshin
  4. Hansa, Ikea, Joshin
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