How many two-digit AB numbers exist for which the difference between AB and BA is 9.

In a two-digit number of the type AB, the first digit means the number of tens in this number, and the second digit means the number of units in this number, therefore, this two-digit number can be written as 10 * A + B.

Then a two-digit number of the form BA can be written in the form 10 * B + A.

According to the condition of the problem, the difference between the number AB and the number BA is 9, therefore, we can write the following ratio:

10 * A + B – 10 * B – A = 9;

9 * A – 9 * B = 9;

9 * (A – B) = 9;

A – B = 1;

A = B + 1.

Therefore, in the desired two-digit number, the first digit is 1 more than the second digit.

There are 8 such two-digit numbers: 21; 32; 43; 54; 65; 76; 87; 98.

Answer: there are 8 such two-digit numbers.