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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