Question - How Many Different Codes Can Be Generated

To determine how many different four-digit capicúa (palindromic) numbers can be formed, we note that in a four-digit number, the first digit must be the same as the fourth, and the second must be the same as the third. Therefore, a four-digit capicúa number can be represented as:

ABBA

Where A and B are digits.

1. The first digit A can be any digit from 1 to 9 (9 options, since it can't be 0).

2. The second digit B can be any digit from 0 to 9 (10 options).

Thus, the total number of different capicúa numbers is given by:

Total = 9 \times 10 = 90