Raghav, Manpreet, Sunaina, Prakrit, Vedika and Arwa are sitting around a circular table facing the centre. Raghav is second to the left of Prakrit. Manpreet is to the immediate left of Sunaina. Arwa is second to the right of Vedika. There are an equal number of persons between Raghav and Manpreet from both the ends. Who is sitting third to the left of Sunanina?
Arwa
Understanding the Circular Seating Arrangement Puzzle
This question involves arranging six people - Raghav, Manpreet, Sunaina, Prakrit, Vedika, and Arwa - around a circular table. They are all facing the centre. We are given several clues about their relative positions. To solve this, we need to use the clues to build the arrangement step-by-step.
Analyzing the Seating Arrangement Constraints
Here are the given conditions:
- Raghav is second to the left of Prakrit: Moving two positions counter-clockwise from Prakrit leads to Raghav. This means one person sits between Prakrit and Raghav on Prakrit's left side.
- Manpreet is to the immediate left of Sunaina: Moving one position counter-clockwise from Sunaina leads to Manpreet. Manpreet is next to Sunaina on Sunaina's left side.
- Arwa is second to the right of Vedika: Moving two positions clockwise from Vedika leads to Arwa. One person sits between Vedika and Arwa on Vedika's right side.
- There are an equal number of persons between Raghav and Manpreet from both the ends: In a circular arrangement of 6 people, if the number of people between two individuals is the same when counted in both directions around the circle, those two individuals are diametrically opposite each other. For 6 people, opposite means they are 3 positions apart, with 2 people between them in each direction.
Building the Circular Table Arrangement
Let's use the constraints to place the six people around the table. We can number the seats 1 through 6 clockwise for clarity.
Deducing Key Positions (Raghav and Manpreet Opposite)
The condition about equal numbers of persons between Raghav and Manpreet from both ends tells us they are opposite. Let's place Raghav first to start building the arrangement.
- Assume Raghav is at seat 1.
- Since Raghav and Manpreet are opposite, Manpreet must be at seat 1 + 3 = seat 4.
Current placement:
| Seat (CW) | Person |
|---|---|
| 1 | Raghav (R) |
| 2 | |
| 3 | |
| 4 | Manpreet (M) |
| 5 | |
| 6 |
Placing Prakrit and Sunaina
Now we use the clues involving Prakrit and Sunaina:
- Raghav (at 1) is second to the left (CCW) of Prakrit: If Raghav is at 1, moving 2 steps counter-clockwise from Prakrit leads to 1. Let Prakrit be at seat 'x'. Moving 1 step CCW from x is x+1, 2 steps CCW is x+2 (all modulo 6, with 6 mapping to 0 or handling wrap-around). So, x+2 = 1 (mod 6). x = 1 - 2 = -1 (mod 6) = 5. So, Prakrit is at seat 5.
- Manpreet (at 4) is immediate left (CCW) of Sunaina: If Manpreet is at 4, moving 1 step counter-clockwise from Sunaina leads to 4. Let Sunaina be at seat 'y'. Moving 1 step CCW from y is y+1 (mod 6). So, y+1 = 4 (mod 6). y = 4 - 1 = 3. So, Sunaina is at seat 3.
Current placement:
| Seat (CW) | Person |
|---|---|
| 1 | Raghav (R) |
| 2 | |
| 3 | Sunaina (S) |
| 4 | Manpreet (M) |
| 5 | Prakrit (P) |
| 6 |
The empty seats are 2 and 6. The remaining people are Vedika and Arwa.
Placing Vedika and Arwa
We use the last positional clue:
- Arwa is second to the right (CW) of Vedika: If Vedika is at seat 'v', moving 1 step CW leads to v-1, and 2 steps CW leads to v-2 (modulo 6, handling wrap-around). Arwa is at seat 'a', so a = v-2 (mod 6).
- The available seats for Vedika and Arwa are 2 and 6.
- Case 1: Vedika is at seat 2. 1st right (CW) of 2 is 1 (Raghav). 2nd right (CW) of 2 is 6. So Arwa must be at seat 6. This fits the remaining seats. (Check: If V=2, A=6. Is A 2nd right of V? V(2) -> 1(R) -> 6(A). Yes.)
- Case 2: Vedika is at seat 6. 1st right (CW) of 6 is 5 (Prakrit). 2nd right (CW) of 6 is 4 (Manpreet). Arwa cannot be Manpreet as Manpreet is already placed. So this case is not possible.
Therefore, Vedika is at seat 2 and Arwa is at seat 6.
Final Seating Arrangement
Combining all the placements, the arrangement (clockwise from seat 1) is:
| Seat Position (Clockwise) | Person |
|---|---|
| 1 | Raghav (R) |
| 2 | Vedika (V) |
| 3 | Sunaina (S) |
| 4 | Manpreet (M) |
| 5 | Prakrit (P) |
| 6 | Arwa (A) |
Verification of Conditions
Let's quickly check if this arrangement satisfies all the initial conditions:
- Raghav (1) is second to the left (CCW) of Prakrit (5)? From P(5), 1st left is at seat 6 (Arwa), 2nd left is at seat 1 (Raghav). Yes, this condition is satisfied.
- Manpreet (4) is immediate left (CCW) of Sunaina (3)? From S(3), 1st left is at seat 4 (Manpreet). Yes, this condition is satisfied.
- Arwa (6) is second to the right (CW) of Vedika (2)? From V(2), 1st right is at seat 1 (Raghav), 2nd right is at seat 6 (Arwa). Yes, this condition is satisfied.
- Raghav (1) and Manpreet (4) are opposite? Yes, seats 1 and 4 are opposite in a 6-seat circle. Yes, this condition is satisfied.
All conditions are met by this arrangement.
Answering the Question: Third to the Left of Sunaina
The question asks who is sitting third to the left of Sunaina.
- Sunaina is at seat 3 in our clockwise numbering.
- Left means moving counter-clockwise (CCW).
- Starting from Sunaina (seat 3):
- 1st to the left is at seat 4 (Manpreet).
- 2nd to the left is at seat 5 (Prakrit).
- 3rd to the left is at seat 6 (Arwa).
The person sitting third to the left of Sunaina is Arwa.
Revision Table: Circular Arrangement Concepts
Here are some key concepts used in solving circular seating arrangement puzzles:
| Concept | Description | Example (6 people) |
|---|---|---|
| Facing Centre | Left is Counter-Clockwise (CCW), Right is Clockwise (CW). | From position 1, 2 is right, 6 is left. |
| Immediate Left/Right | The person in the very next seat in the specified direction. | Immediate left of 3 is 4 (CCW). Immediate right of 3 is 2 (CW). |
| Nth Left/Right | Move N steps in the specified direction. | 2nd left of 3: 1st left is 4, 2nd left is 5 (CCW). |
| Opposite Positions | For an even number of seats (N), two seats are opposite if they are N/2 positions apart. | In a 6-seat circle, seats 1 & 4, 2 & 5, 3 & 6 are opposite. |
| "Between" Constraint | Specifies the number of people separating two individuals in one or both directions. "Equal number from both ends" implies opposite in a circle. | 2 people between R and M from both ends means R and M are opposite. |
Additional Information: Seating Puzzle Strategies
Solving seating arrangement puzzles requires careful reading and systematic placement. Here are some tips:
- Start with the most definitive clues, such as "immediate left/right" or "opposite," as these fix relative positions more rigidly.
- Represent the circle visually or use numbered positions. Be consistent with your definition of left (CCW) and right (CW).
- Break down complex constraints (like "second to the left") into steps.
- Note down the placement of each person as you deduce it.
- If multiple possibilities arise (e.g., for the last few people), test each possibility against all remaining constraints.
- Always verify your final arrangement against all the initial conditions to ensure correctness.
- Pay close attention to the exact wording, especially "to the left/right of" vs. "between".
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