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?

Correct Answer: Four

Let us solve this puzzle step-by-step to find the order in which seven persons (A, B, C, D, E, F, and G) go to watch the puppet show, from 1st to 7th.

Step 1: Analyze the given conditions
1. Seven persons go one after another (Positions 1 to 7).
2. "D goes to the puppet show three persons before C."
This means there are two persons between D and C (Order: D, _, _, C).
3. "One person goes between C and G."
This gives two possibilities for G relative to C: (D, G, _, C) or (D, _, _, C, _, G).
4. "As many persons go after G, as before F."
This implies that the position of F from the start (1st) is symmetrical to the position of G from the end (7th). That is:
$\text{Position of F}=8-\text{Position of G}$
5. "F doesn’t go first to watch the puppet show." (F ≠ Position 1, which means G ≠ Position 7).
6. "B goes immediately before A." (Order: B, A together).

Step 2: Determine the positions
Let us test the possible positions for D and C:

Case 1: D is at Position 1
- If D = 1, then C = 4.
- Since one person goes between C and G, G can be at Position 2 or Position 6.
- If G = 2: Then 5 persons go after G, so 5 persons must go before F ⇒ F = 6.
- Now, positions remaining: 3, 5, 7.
- We need two adjacent positions for B and A (B immediately before A). The available positions are 3, 5, 7, which are not adjacent! So G cannot be 2.
- If G = 6: Then 1 person goes after G, so 1 person must go before F ⇒ F = 2.
- Now, positions occupied: D(1), F(2), C(4), G(6).
- Remaining positions: 3, 5, 7. Again, no two adjacent positions left for (B, A). Thus, Case 1 fails.

Case 2: D is at Position 2
- If D = 2, then C = 5.
- One person goes between C and G, so G can be at Position 3 or Position 7.
- But F cannot be first (F ≠ 1), which means G cannot be at Position 7 (since if G=7, 0 persons after G, so 0 persons before F ⇒ F=1). Thus, G must be at Position 3.
- If G = 3: 4 persons go after G (4, 5, 6, 7), so 4 persons must go before F ⇒ F = 5. But C is already at Position 5! Contradiction. Thus, Case 2 fails.

Case 3: D is at Position 3
- If D = 3, then C = 6.
- One person goes between C and G, so G can be at Position 4.
- If G = 4: 3 persons go after G (5, 6, 7), so 3 persons go before F ⇒ F = 4. But Position 4 is already occupied by G! Contradiction. Thus, Case 3 fails.

Case 4: D is at Position 4
- If D = 4, then C = 7.
- One person goes between C and G ⇒ G = 5.
- Since G is at Position 5, 2 persons go after G (6 and 7). Therefore, 2 persons must go before F ⇒ F = 3.
- Now, occupied positions so far: F(3), D(4), G(5), C(7).
- Remaining empty positions: 1, 2, 6.
- "B goes immediately before A": Positions 1 and 2 are vacant and adjacent, so B = 1 and A = 2.
- The only remaining position is 6, which must be filled by E ⇒ E = 6.

Final Order of Persons (1 to 7):
1 - B
2 - A
3 - F
4 - D
5 - G
6 - E
7 - C

Step 3: Answer the question
The question asks: "How many persons go between A and C?"
- A is at Position 2.
- C is at Position 7.
- The persons between A (Position 2) and C (Position 7) are F (3), D (4), G (5), and E (6).
- Thus, there are 4 (Four) persons between A and C.