Who are the neighbours of S2?
Step 1: Determine the Middle Position
Seven friends are sitting in a row. The middle position in a row of 7 is the 4th position. S2 is located at this position.
Arrangement: $_ _ _ S2 _ _ _$
Step 2: Locate S5 and S7
There are 3 friends between S5 and S7. This implies their positions could be {1, 5}, {2, 6}, or {3, 7}.
Both S5 and S7 are not at the extreme ends (positions 1 and 7).
Combining these conditions, the only possible positions for S5 and S7 are 2 and 6.
Step 3: Determine S3's Position
There are 2 friends between S3 and S5.
Case A: If S5 is at position 2.
- The arrangement is $_ S5 _ S2 _ S7 _$.
- To place 2 friends between S3 and S5(2), S3 must be at position 5. (Friends at positions 3 and 4).
- Partial arrangement: $_ S5 _ S2 S3 S7 _$
Case B: If S5 is at position 6.
- The arrangement is $_ S7 _ S2 _ S5 _$.
- To place 2 friends between S3 and S5(6), S3 must be at position 3. (Friends at positions 4 and 5).
- Partial arrangement: $_ S7 S3 S2 _ S5 _$
Step 4: Place S4 and Finalize Arrangement
S4 is not at any extreme end (positions 1 and 7).
Consider Case A (S5 at 2, S3 at 5, S7 at 6):
- Arrangement: $_ S5 _ S2 S3 S7 _$
- Remaining positions: 1, 3, 7. Remaining friends: S1, S4, S6.
- Since S4 cannot be at ends 1 or 7, S4 must be at position 3.
- Final arrangement: $S1/S6 S5 S4 S2 S3 S7 S1/S6$
- The neighbors of S2 (at position 4) are the individuals at positions 3 and 5, which are S4 and S3.
Consider Case B (S7 at 2, S3 at 3, S5 at 6):
- Arrangement: $_ S7 S3 S2 _ S5 _$
- Remaining positions: 1, 5, 7. Remaining friends: S1, S4, S6.
- Since S4 cannot be at ends 1 or 7, S4 must be at position 5.
- Final arrangement: $S1/S6 S7 S3 S2 S4 S5 S1/S6$
- The neighbors of S2 (at position 4) are the individuals at positions 3 and 5, which are S3 and S4.
Step 5: Identify Neighbors of S2
Both valid seating arrangements consistently show that S3 and S4 are the immediate neighbors of S2.
Similar Questions
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- Study the given information carefully and answer the question that follows.
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Where is R sitting?
Important Questions from Linear Arrangement
Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Six people P, Q, R, S, T and U sit in a row, not necessarily in the same order. If two persons sit in between P and Q, and two persons sit in between T and U, then how many persons sit in between R and S?
Six persons P, Q, R, S, T and U are sitting in a row facing north (not necessarily in the same order). Q sits fourth to the right of S. One person sits between P and Q. Three persons sit between R and T. R sits immediate left of P. How many persons sit between T and U?
