Choose a two-digit number and do the following: if the number is odd, add one to it; If the number is even, you divide it by two. With the result, we do the same, and repeat until we get 1. With what two-digit number do we get the longest sequence? Why is that number?

Let's analyze the sequence for the number 97: Starting with 97: Since 97 is odd, we add one to get 98. 98 is even, so we divide by two to get 49. 49 is odd, so we add one to get 50. 50 is even, so we divide by two to get 25. 25 is odd, so we add one to get 26. 26 is even, so we divide by two to get 13. 13 is odd, so we add one to get 14. 14 is even, so we divide by two to get 7. 7 is odd, so we add one to get 8. 8 is even, so we divide by two to get 4. 4 is even, so we divide by two to get 2. 2 is even, so we divide by two to get 1. The sequence for the number 97 is also 12 steps long. 97 result in the longest sequences when applying the given process among two-digit numbers, each with a sequence length of 12. This is due to the alternating odd and even operations that prolong the process before reaching 1.