Solution
Understanding the set :-
- A game - CHANGO - played between two players ( one of them wins and the other loses, i.e., there are no drawn)
- 12 players participated and divided into four groups :
Group A consisted of Aruna, Azul, and Arif
Group B consisted of Brinda, Brij, and Biju
Group C consisted of Chitra, Chetan, and Chhavi
Group D consisted of Dipen, Donna, and Deb.
- Players within each group had a distinct rank
- In the group stage of the game, the second and third ranked players play against each other, and the winner of that game plays against the first ranked player of the group
- The winner of this second game is considered as the winner of the group and enters a semi-final.
This is a games and tournament set,
In this type of sets you will very often find different types of games with different number of rounds and have to find the winner or loser.
The most important thing to understand here is to look out for the rules of the game given in the set very carefully, as these will be the base point to start the set or to form a table.
CONCEPTUAL CLARITY :-
| Players | Aruna | Azul | Arif |
|---|---|---|---|
| Aruna | x | ||
| Azul | x | ||
| Arif | x |
This is a standard games and tournament table,
Let's first understand the table,
First row gives information about Aruna,
When Aruna (row 1) plays with Azul (column 2)
the result will be written here.
Let's taken an example, we need to record that When there was a match between Aruna and Arif, Aruna won
=> Arif lost to Arun so that will be recorded as :
| Players | Aruna | Azul | Arif |
|---|---|---|---|
| Aruna | x | W | |
| Azul | x | ||
| Arif | L | x |
Here it shows Aruna won (W) to Arif
and, Arif lost (L) to Aruna.
Therefore, in this table every point will have two entry
as if someone is winning then there will be other who is losing.
Group A :-
| Players | Aruna | Azul | Arif |
|---|---|---|---|
| Aruna ( 1 ) | x | x | |
| Azul | x | ||
| Arif | x | x |
Clue 3 says,
Aruna, Biju, Chitra, and Dipen played three games each,
Since, Since Aruna played 3 games if she belongs to rank 2 or rank 3 in her group she must have reached the semifinals and lost in the semifinals
But for this case, she must play against rank 1 and rank 3 in her group.
But clue 2 says,
she did not play against Arif from her group
Hence Aruna was ranked 1 in her group.
| Players | Aruna | Azul | Arif |
|---|---|---|---|
| Aruna ( 1 ) | x | W | x |
| Azul ( 2 ) | L | x | W |
| Arif ( 3 ) | X | L | x |
Among Azul and Arif one of them was ranked 2 and the other was ranked 3.
Azul defeated Arif in the first round and in the second round lost to Aruna.
Aruna played her first round with Azul and won the round and played against the winner from group B and defeated them and moved to the finals.
These were the 3 matches of Aruna.
Group B :-
| Players | Brinda | Brij | Biju |
|---|---|---|---|
| Brinda (2/3) | x | x | L |
| Brij (2/3) | x | x | L |
| Biju ( 1) | W | W | x |
Clue 2,
Brij did not play against Brinda.
Clue 3,
Biju played 3 games., Brij and Brinda played one game each
Since Brij and Brinda played only one game each one of them was ranked 1 and the other was ranked 2 and 3.
Brij did not play against Brinda.
We are aware that Aruna reached finals
We are aware that Aruna reached finals and hence the person from Group B did not reach the finals.
Biju played three games and hence must have played with Brij/Brinda in the first round and won the round.
Plays with Brij/ Brinda and wins the second round. Plays with Aruna and loses the third round.
Group c :-
| Players | Chitra | Chetan | Chhavi |
|---|---|---|---|
| Chitra (1) | x | W | W |
| Chetan | L | x | W |
| Chhavi | L | L | x |
Clue 3,
Chitra played 2 matches and Chetan played 2 matches.
For Chitra to play 2 matches if she is rank 2 or rank 3 in her group.
She must at least reach the semifinals.
But in this case, Chetan will be defeated in his first round.
So Chitra must be ranked 1 in her group and Chetan must be ranked 2 or rank 3 in his group.
He defeats Chhavi in his first round and loses to Chitra in his second round.
Chitra plays Chetan in her first round, wins over the winner of group D in her second round, and loses in the final against Aruna as per condition 1.
Group D :-
The person from Group D did not reach the finals because Chitra reached the finals.
In order for Dipen to play 3 matches before his finals.
Dipen must be ranked 2 or rank 3 in his group and plays Deb and Donna in the first two rounds in any order and wins over both of them.
Dipen loses to Chitra in his third round.
Final Configuration :-
| Group - A | Group - B |
|---|---|
| Aruna vs Biju | |
| Azul vs Aruna | Biju vs Brinda / Brij |
| Azul vs Arif | Biju vs Brinda / Brij |
| Group - C | Group - D |
|---|---|
| Chitra vs Dipen | |
| Chetan vs Chitra | Dipen vs Deb/Donna |
| Chetan vs Chavvi | Dipen vs Deb/Donna |
Aruna plays Chitra in the finals and wins the final round.
Final Configuration :-
| Group - A | Group - B |
|---|---|
| Aruna vs Biju | |
| Azul vs Aruna | Biju vs Brinda / Brij |
| Azul vs Arif | Biju vs Brinda / Brij |
| Group - C | Group - D |
|---|---|
| Chitra vs Dipen | |
| Chetan vs Chitra | Dipen vs Deb/Donna |
| Chetan vs Chavvi | Dipen vs Deb/Donna |
Aruna plays Chitra in the finals and wins the final round.
Chitra, Dipen