In the following series, how many such odd numbers are there which are divisible by $3$ or $5$, then followed by odd numbers, and then also followed by even numbers?
$$\text{12, 19, 21, 3, 25, 18, 35, 20, 22, 21, 45, 46, 47, 48, 9, 50, 52, 54, 55, 56}$$

We need to look for a triplet pattern:
$$\text{[Odd number divisible by 3 or 5]}\to \text{[Odd Number]}\to \text{[Even Number]}$$

Let's check the odd numbers divisible by $3$ or $5$:

*$21$ **: Followed by $3$ (odd), which is followed by $25$ (odd). Does not match (Odd-Odd-Odd).
*$3$ **: Followed by $25$ (odd), which is followed by $18$ (even). Pattern: $3\to 25\to 18$. $\to$ Valid (1)
*$25$ **: Followed by $18$ (even). Invalid.
*$35$ **: Followed by $20$ (even). Invalid.
*$21$ **: Followed by $45$ (odd), which is followed by $46$ (even). Pattern: $21\to 45\to 46$. $\to$ Valid (2)
*$45$ **: Followed by $46$ (even). Invalid.
*$9$ **: Followed by $50$ (even). Invalid.
*$55$ **: Followed by $56$ (even). Invalid.

Hence, there are exactly two such numbers ($3$ and $21$).