Solution
Understanding the set :
This is an arrangement set,
Here there are four performers - Princess, Queen, Rani and Samragni and four composers - Ashman, Badal, Gagan and Dyu.
We need to find the sequence in which dancers have performed and also, there composers.
In this set most important clues are :
- The dancers performed their second items in the same sequence of their performance of their first items.
- No dancer performed her second item before the performance of the first item by any other dancers.
- The items performed by the four dancers were all assigned by different music composers.
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | Princess | Badal |
| 6 | ||
| 7 | ||
| 8 |
Clue 3 says,
The first performance was by Princess; this item was assigned by Badal.
We can directly add this to the table.
Also, we are given that,
The dancers performed their second items in the same sequence of their performance of their first items.
=> 1st performance of second item will also be of princess.
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | ||
| 3 | ||
| 4 | Rani | |
| 5 | Princess | |
| 6 | ||
| 7 | ||
| 8 | Rani | Gagan |
Clue 4 says,
The last performance was by Rani; this item was assigned by Gagan.
This also can be directly added to the table.
And, since, second items are performed in the same sequence as their first items.
=> 4th performance is also of Rani.
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | ||
| 3 | ||
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | ||
| 7 | ||
| 8 | Rani | Gagan |
Using clue 5 ;
The items assigned by Ashman were performed consecutively.
We know, items performed by the four dancers were all assigned by different music composers
=> Ashman can compose consecutively only as last item of 1st performance (4th) and first item of 2nd performance (5th).
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Queen | |
| 3 | Samragni | |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Queen | |
| 7 | Samragni | |
| 8 | Rani | Gagan |
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Samragni | |
| 3 | Queen | |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Samragni | |
| 7 | Queen | |
| 8 | Rani | Gagan |
Now, we only have to find Queen and Samragni's position.
Therefore, let's make two cases :
CASE - 1 - when 2nd item is by Queen
CASE - 2 - when 2nd item is performed by Samragni
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Queen | |
| 3 | Samragni | |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Queen | Dyu |
| 7 | Samragni | Badal |
| 8 | Rani | Gagan |
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Samragni | |
| 3 | Queen | |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Samragni | Badal |
| 7 | Queen | Dyu |
| 8 | Rani | Gagan |
Now, clue 1 says,
No composer who assigned item to Princess, assigned any item to Queen.
=> In 2nd performance,
Queen can't have Badal as composer
Therefore, Badal will compose for Samragni in 2nd performance.
=> Dyu will compose for Queen in 2nd performance.
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Queen | Gagan |
| 3 | Samragni | Dyu |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Queen | Dyu |
| 7 | Samragni | Badal |
| 8 | Rani | Gagan |
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Samragni | Dyu |
| 3 | Queen | Gagan |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Samragni | Badal |
| 7 | Queen | Dyu |
| 8 | Rani | Gagan |
Now, in 1st performance ,
Dyu will assign to Samragni
As, Dyu has already assigned for queen in second performance, therefore, Dyu can't assign to queen again in first performance.
And, Gagan will assign to Queen .
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Queen | Gagan |
| 3 | Samragni | Dyu |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Queen | Dyu |
| 7 | Samragni | Badal |
| 8 | Rani | Gagan |
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Samragni | Dyu |
| 3 | Queen | Gagan |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Samragni | Badal |
| 7 | Queen | Dyu |
| 8 | Rani | Gagan |
Now, we are given that - The number of performances between items assigned by each of the remaining composers was the same.
In case 1 -
performances between items assigned by Badal = 5
But , performance between Dyu is 2.
Therefore, Case is rejected.
| Slot | Dancer | Composer |
|---|---|---|
| 1 | Princess | Badal |
| 2 | Samragni | Dyu |
| 3 | Queen | Gagan |
| 4 | Rani | Ashman |
| 5 | Princess | Ashman |
| 6 | Samragni | Badal |
| 7 | Queen | Dyu |
| 8 | Rani | Gagan |
Queen did not perform in any item composed by Gagan is a false statement , as Queen has performed in her 1st performance by item composed by Gagan.