Study the following information carefully and answer the questions given below.
Seven persons – A, B, C, D, E, F and G go to watch a puppet show one after another but not necessarily in the same order.
D goes to the puppet show three persons before C. One person goes between C and G. As many persons go after G, as before F. F doesn’t go first to watch the puppet show. B goes immediately before A.

How many persons go between A and C?

The correct option is Four.

Step-by-step Explanation:

Let us arrange the seven persons (A, B, C, D, E, F, G) in order from 1 to 7 based on the given clues:

1. "D goes to the puppet show three persons before C."
This means D and C have two persons between them in the pattern: D, _, _, C.

2. "One person goes between C and G."
So, G can be either 2 positions after C (D, _, _, C, _, G) or 2 positions before C (D, G, _, C).

3. "As many persons go after G, as before F."
This means the position of F from the start is equal to the position of G from the end (Position of F = 8 - Position of G).

4. "F doesn’t go first to watch the puppet show."
So, F cannot be at position 1. Therefore, G cannot be at position 7.

5. "B goes immediately before A."
This means B and A form a consecutive block: (B, A).

Let us analyze the possibilities:

Case 1: G is after C (D, _, _, C, _, G)
Since there are 7 positions total, D must be at position 1 or 2.
- If D is at position 1: Sequence is D(1), _, _, C(4), _, G(6).
Since G is 6th (2nd from end), F must be 2nd from start (position 2).
So, the arrangement becomes: 1: D, 2: F, 3: _, 4: C, 5: _, 6: G, 7: _.
Now we need to place the (B, A) block in consecutive empty positions. The remaining empty positions are 3, 5, and 7. There are no two adjacent empty positions available for (B, A). So this sub-case is invalid.

- If D is at position 2: Sequence is _, D(2), _, _, C(5), _, G(7).
Here G is at position 7, which would mean F is at position 1. But F cannot go first. So this sub-case is invalid.

Case 2: G is before C (D, G, _, C)
D and C have two persons between them, and G is one person before C.
Let us check the possible positions for D, G, C:

- If D is at position 1:
Positions: 1: D, 2: G, 3: _, 4: C.
Since G is at position 2 (6th from end), F must be 6th from start (position 6).
Positions: 1: D, 2: G, 3: _, 4: C, 5: _, 6: F, 7: _.
Now we need to place the (B, A) block in consecutive empty positions. The empty positions are 3, 5, and 7, which are not adjacent. Thus, no space for (B, A).

- If D is at position 2:
Positions: 1: _, 2: D, 3: G, 4: _, 5: C.
Since G is at position 3 (5th from end), F must be at position 5. But C is already at position 5! So this is invalid.

- If D is at position 3:
Positions: 1: _, 2: _, 3: D, 4: G, 5: _, 6: C, 7: _.
Since G is at position 4 (4th from end), F must be at position 4. But G is at position 4! So this is invalid.

Wait, let's re-verify G being after C when D is at position 1:
D at 1: D(1), _(2), _(3), C(4), _(5), G(6), _(7).
G is 6th, so F is 2nd.
Remaining positions: 3, 5, 7. E, B, A must fit. If B, A are consecutive, let me re-check positions:
If G is after C with one person between C and G:
Positions: C, _, G -> if C is 4, G is 6.
What if G is before C with one person between C and G?
Sequence: G, _, C (one person between G and C).
Since D is 3 persons before C: D, _, _, C.
Comparing (D, _, _, C) and (G, _, C):
Position of C = Position of D + 3.
Position of G = Position of C - 2 = Position of D + 1.
So the order is: D, G, _, C.
Let me re-evaluate D at position 1 for D, G, _, C:
1: D, 2: G, 3: _, 4: C.
G is at 2, so number of persons after G is 5 (positions 3,4,5,6,7).
Number of persons before F must also be 5, so F is at position 6.
Remaining slots for (B, A) block and E are 3, 5, 7 (not adjacent).

What if G is after C? "One person goes between C and G."
Sequence: C, _, G.
D, _, _, C, _, G.
Positions required: 6 contiguous spots.
If D is at 1: 1: D, 2: _, 3: _, 4: C, 5: _, 6: G, 7: _.
Number of persons after G = 1 (position 7).
Number of persons before F = 1, so F is at position 2!
Positions occupied: 1: D, 2: F, 4: C, 6: G.
Empty positions: 3, 5, 7.
Since B goes immediately before A, they need two adjacent empty positions. Slots 3, 5, 7 are not adjacent.

Wait! Let me re-read: "D goes to the puppet show three persons before C."
"Three persons before C" means there are 2 persons between D and C, or is it 3 persons before C (meaning D is 3rd before C, i.e., D, _, _, C)?
In puzzle terminology, "3 persons before C" means D is at (Position of C - 3). Yes, so 2 persons between them.
What if D is at position 1, and B, A are at 6, 7?
Wait! Let me check if G is before C:
If G is 1st: 1: G, 2: D, 3: C (not fitting D, _, _, C).
Let's check D at 2, C at 5, G at 3 (G before C):
1: _, 2: D, 3: G, 4: _, 5: C.
Persons after G = 4 (positions 4,5,6,7).
Persons before F = 4, so F is at position 5. But C is at 5. (Invalid)

Let's check D at 1, C at 4, G at 2:
1: D, 2: G, 3: _, 4: C.
Persons after G (2) = 5.
Persons before F = 5 => F is at 6.
Slots available: 3, 5, 7.
Wait, what if B, A are at 4, 5? But C is at 4.

Let's check if D is at 3, C at 6, G at 4:
1: _, 2: _, 3: D, 4: G, 5: _, 6: C, 7: _.
Persons after G (4) = 3.
Persons before F = 3 => F is at 4, but G is at 4. (Invalid)

What if D is at 4, C at 7, G at 5?
1: _, 2: _, 3: _, 4: D, 5: G, 6: _, 7: C.
Persons after G (5) = 2.
Persons before F = 2 => F is at position 3.
Positions occupied: 3: F, 4: D, 5: G, 7: C.
Empty positions: 1, 2, 6.
Positions 1 and 2 are adjacent! So B and A can be placed at 1 and 2 respectively (B at 1, A at 2)!
Let's check this arrangement:
1: B
2: A
3: F
4: D
5: G
6: E
7: C

Let's double check all conditions for this arrangement:
1. 7 persons: B, A, F, D, G, E, C.
2. "D goes to the puppet show three persons before C": D is at 4, C is at 7 (4 is 3 positions before 7). Correct!
3. "One person goes between C and G": C is at 7, G is at 5. One person (E at 6) is between them. Correct!
4. "As many persons go after G, as before F": G is at 5, so 2 persons go after G (6 and 7). F is at 3, so 2 persons go before F (1 and 2). Correct!
5. "F doesn’t go first": F is 3rd. Correct!
6. "B goes immediately before A": B is 1st, A is 2nd. Correct!

Final Order:
1 - B
2 - A
3 - F
4 - D
5 - G
6 - E
7 - C

Question: How many persons go between A and C?
A is at position 2 and C is at position 7.
The persons between A and C are F (3), D (4), G (5), and E (6).
Total number of persons between A and C = 4.