Eight persons — A, B, C, D, E, F, G and H — were born on two different dates i.e. 5th and 12th of four different months viz. January, March, April and June of the same year. No two persons were born on the same day.

C was born on an odd date in the month having even number of days. Three persons were born between C and F. As many persons were born before F as after B. Four persons were born between D and B. G was born immediately before D. A was born on an odd date. E was born before H.

How many persons were born between A and D?

To determine the number of persons born between A and D, let us systematically analyze the given information and construct the birth schedule of the eight persons.

The months and dates given are:
- January (31 days): 5th, 12th
- March (31 days): 5th, 12th
- April (30 days): 5th, 12th
- June (30 days): 5th, 12th

This gives us 8 positions in chronological order:
1. January 5th
2. January 12th
3. March 5th
4. March 12th
5. April 5th
6. April 12th
7. June 5th
8. June 12th

Let's analyze the clues step-by-step:

Clue 1: "C was born on an odd date in the month having even number of days."
The months with an even number of days (30 days) are April and June.
The odd date is the 5th.
Therefore, C was born on either April 5th or June 5th.

Clue 2: "Three persons were born between C and F."
- Case 1: If C is born on April 5th (Position 5):
Three persons between C and F means F can be at Position 1 (January 5th) because there are 3 positions (Position 2, 3, 4) in between.
- Case 2: If C is born on June 5th (Position 7):
Three persons between C and F means F must be at Position 3 (March 5th) because there are 3 positions (Position 4, 5, 6) in between.

Clue 3: "As many persons were born before F as after B."
- In Case 1 (F at Position 1):
Number of persons born before F is 0. So, the number of persons born after B must also be 0, which places B at Position 8 (June 12th).
- In Case 2 (F at Position 3):
Number of persons born before F is 2 (Positions 1 and 2). So, the number of persons born after B must be 2, which places B at Position 6 (April 12th).

Clue 4: "Four persons were born between D and B."
- In Case 1 (B at Position 8):
Count backwards 4 positions from B: Positions 7, 6, 5, 4. This places D at Position 3 (March 5th).
- In Case 2 (B at Position 6):
We cannot place D. Counting forwards or backwards is not possible to have 4 persons in between because the total positions are 8 (from 6, counting back 4 positions: 5, 4, 3, 2, which would put D at Position 1. Let's check: between Position 1 and Position 6, the positions are 2, 3, 4, 5, which is exactly 4 positions. So D would be at Position 1. Let's verify Case 2 with the next clue).

Clue 5: "G was born immediately before D."
- In Case 1 (D at Position 3):
G must be at Position 2 (January 12th). This is valid.
- In Case 2 (D at Position 1):
G cannot be placed because there is no position before Position 1. Thus, Case 2 is eliminated.

Now, let's complete the schedule for Case 1:
- Position 1 (Jan 5): F
- Position 2 (Jan 12): G
- Position 3 (Mar 5): D
- Position 4 (Mar 12): [Empty]
- Position 5 (Apr 5): C
- Position 6 (Apr 12): [Empty]
- Position 7 (Jun 5): [Empty]
- Position 8 (Jun 12): B

Clue 6: "A was born on an odd date."
The remaining empty positions are Position 4 (March 12th - even date), Position 6 (April 12th - even date), and Position 7 (June 5th - odd date).
Since A was born on an odd date, A must be at Position 7 (June 5th).

Clue 7: "E was born before H."
The remaining empty positions are Position 4 and Position 6.
Since E was born before H, E must be at Position 4 (March 12th) and H must be at Position 6 (April 12th).

The final arrangement is:
1. January 5th: F
2. January 12th: G
3. March 5th: D
4. March 12th: E
5. April 5th: C
6. April 12th: H
7. June 5th: A
8. June 12th: B

Now, let us find the number of persons born between A and D:
A was born on June 5th (Position 7) and D was born on March 5th (Position 3).
The persons born between them are E (March 12th), C (April 5th), and H (April 12th).
Thus, there are exactly three persons born between A and D.