A numerical sequence is called a SEQUENLADA when, starting from the second number, the next element is formed by the rules:

I) if it has more than 2 digits, the last digit is moved to the $1 \underline{st}$ position and then the two last digits are added;

II) if it has two digits, these 2 are added until a single digit is obtained.

The sequence ends when we reach a number with only one digit. An example of a SEQUENLADA is:

$$
Solution

a) $246.831 \rightarrow 124.611 \rightarrow 11.247 \rightarrow 5.443 \rightarrow 358 \rightarrow 88 \rightarrow 16 \rightarrow 7$.

b) Let's analyze the sequence in reverse, with the first number being 1. The second number can only be 10 or 100. In the first case (10), the $3^{\text{rd}}$ term can be $19, 28, 37, 46, 55, 64, 73, 82, 91, 190, 280, 370, 460, 550, 640, 730, 820, 910$, or 1,000; in the second case (100 in the second position), the $3^{\text{rd}}$ number in the sequence can only be 10,000.

Let's organize the sequences:

| 19 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| :---: | :---: | :---: | :---: | :---: |
| 28 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 37 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 46 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 55 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 64 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 73 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 82 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 91 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 190 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 280 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 370 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 460 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 550 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 640 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 730 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 820 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 910 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 1,000 | $\rightarrow$ | 10 | $\rightarrow$ | 1 |
| 10,000 | $\rightarrow$ | 100 | $\rightarrow$ | 1 |

Therefore, there are 20 SEQUENCES with 3 numbers that end in 1.