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.

Who is the last person to go to watch the puppet show?

Correct Answer: The one who goes two persons after G

Let us solve the puzzle step-by-step to find the exact order of the seven persons (positions 1 to 7) going to watch the puppet show.

Step 1: Analyze the given conditions
1. Total persons = 7 (Positions 1, 2, 3, 4, 5, 6, 7 from first to last).
2. "D goes three persons before C" means D is placed 3 positions before C. If C is at position $x$, then D is at position $x-3$ (there are 2 persons between D and C).
3. "One person goes between C and G" means G is either 2 positions before C or 2 positions after C.
4. "As many persons go after G, as before F" gives the relation:

$\text{Persons after G}=\text{Persons before F}$

In terms of position numbers:

$7-\text{Position of G}=\text{Position of F}-1$

$\text{Position of F}+\text{Position of G}=8$

5. F does not go first, so F is not at position 1 (which also means G cannot be at position 7).
6. "B goes immediately before A" means B and A form a contiguous pair (B, A).

Step 2: Test possible positions for D and C
Since D is 3 persons before C, the possible (D, C) position pairs are (1, 4), (2, 5), (3, 6), or (4, 7).

• Case 1: D at 1, C at 4
Since one person is between C and G, G could be at 2 or 6.
- If G = 2, then F = 8 - 2 = 6. The vacant spots are 3, 5, and 7. There are no two adjacent spots for (B, A), so this is invalid.
- If G = 6, then F = 8 - 6 = 2. The vacant spots are 3, 5, and 7. Again, no two adjacent spots for (B, A), so this is invalid.

• Case 2: D at 2, C at 5
G cannot be 7 (since F ≠ 1), so G must be at 3. Then F = 8 - 3 = 5. But position 5 is already occupied by C. Thus, this case is invalid.

• Case 3: D at 3, C at 6
G must be at 4. Then F = 8 - 4 = 4. But position 4 is already occupied by G. Thus, this case is invalid.

• Case 4: D at 4, C at 7
Since C = 7, G must be 2 positions before C, so G = 5.
Using $\text{Position of F}+\text{Position of G}=8$, we get:

$\text{Position of F}=8-5=3$

So far, the filled positions are:
- Position 3: F
- Position 4: D
- Position 5: G
- Position 7: C
The vacant positions are 1, 2, and 6.
Since B goes immediately before A, B and A must take the adjacent vacant positions 1 and 2 respectively.
- Position 1: B
- Position 2: A
The remaining person, E, takes Position 6.

Step 3: Final Arrangement
1. B
2. A
3. F
4. D
5. G
6. E
7. C

Step 4: Identify the Last Person
The last person to go to watch the puppet show (at position 7) is C.
Checking the options:
G is at position 5. The person who goes two persons after G is at position:

$5+2=7$

This position belongs to C.
Therefore, the correct option is The one who goes two persons after G.