Read the given information carefully and answer the questions given below:
14 persons sit in two parallel rows containing seven persons in each row. A, B, C, D, E, F and G – sit in row 1 and face north while P, Q, R, S, T, U and V – sit in row 2 and face south. But not necessarily in the same order. Persons of row 1 face the persons of row 2.
Three persons sit between B and D. D sits at one of the ends. Two persons sit between Q and the one who faces B. One person sits between Q and T. U sits fourth to the right of S but does not sit opposite to D. One person sits between A and the one who faces S. G sits immediate right of C. P does not face C. Number of persons sit to the right of F and V are equal.
How many persons sit between R and P?
Correct Answer :
Three
Solution :
To solve this puzzle, let us represent the positions in each row from 1 to 7 (from left to right, from the perspective of an observer looking at the diagram).
Row 1 faces North (Left is 1, Right is 7).
Row 2 faces South (Left is 1, Right is 7, but from their perspective, Right is towards 1 and Left is towards 7).
Step 1: Determine the positions of B and D in Row 1
Three persons sit between B and D, and D sits at one of the ends (either 1 or 7).
- Case 1: If D is at position 1, then B must be at position 5.
- Case 2: If D is at position 7, then B must be at position 3.
Step 2: Place Q and T in Row 2
Two persons sit between Q and the one who faces B.
- In Case 1 (B is at 5), the one who faces B is at position 5. Q must be at position 2.
- In Case 2 (B is at 3), the one who faces B is at position 3. Q must be at position 6.
One person sits between Q and T.
- In Case 1 (Q is at 2), T must be at position 4.
- In Case 2 (Q is at 6), T must be at position 4.
Step 3: Analyze the positions of U and S in Row 2
Row 2 faces South, so the "right" of a person is towards position 1.
U sits fourth to the right of S, which means:
Position of U = Position of S - 4
Also, U does not sit opposite to D.
- Testing Case 1: D is at 1, B is at 5, Q is at 2, T is at 4.
Since Q is at 2 and U cannot sit opposite to D (position 1), U can only be at position 3, which makes S at position 7.
Now, we are given: "One person sits between A and the one who faces S."
S is at 7, so the one facing S is at position 7. One person sits between A and position 7, meaning A must be at position 5. However, B is already at position 5, which creates a conflict. Thus, Case 1 is invalid.
- Testing Case 2: D is at 7, B is at 3, Q is at 6, T is at 4.
Since Q is at 6, S cannot be at 6. The possible positions for (U, S) are:
- If S is at 5, U is at 1.
- If S is at 7, U is at 3.
Let's check if S is at 5 and U is at 1: The one facing S is at position 5. One person sits between A and position 5, meaning A must be at position 3 or 7. But B is at 3 and D is at 7, so this is impossible.
Therefore, S must be at position 7 and U must be at position 3.
Step 4: Place the remaining persons in Row 1
Row 2 positions currently filled: U (3), T (4), Q (6), S (7).
Row 1 positions currently filled: B (3), D (7).
The one facing S is at position 7 (D). One person sits between A and D, so A must be at position 5.
"G sits immediate right of C." Since Row 1 faces North, G is to the right of C. The only consecutive empty spots in Row 1 are 1 and 2. Therefore, C is at position 1 and G is at position 2.
The remaining empty positions in Row 1 are 4 and 6, to be occupied by E and F.
Step 5: Apply the final constraints
"Number of persons sit to the right of F and V are equal."
Since F faces North (Row 1), the number of persons to the right of F is:
7 - Position of F
Since V faces South (Row 2), the number of persons to the right of V is:
Position of V - 1
So, we have:
7 - Position of F = Position of V - 1
Position of F + Position of V = 8
Since F can be at position 4 or 6:
- If F is at 4, V must be at 4. But T is already at position 4 in Row 2.
- If F is at 6, V must be at 2. Since position 2 in Row 2 is vacant, this is correct. Hence, F is at 6 (which leaves E at 4) and V is at 2.
Now, the remaining positions in Row 2 are 1 and 5, to be filled by P and R.
"P does not face C." Since C is at position 1, P cannot be at position 1. Thus, P is at position 5, and R is at position 1.
Final Arrangement:
Row 2 (South-facing): 1: R, 2: V, 3: U, 4: T, 5: P, 6: Q, 7: S
Row 1 (North-facing): 1: C, 2: G, 3: B, 4: E, 5: A, 6: F, 7: D
Conclusion:
R is at position 1 and P is at position 5.
The persons sitting between R and P are V (2), U (3), and T (4).
Therefore, exactly Three persons sit between R and P.
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