Great dates to solve (maths)

Do you mean:
- exchanged day and month (the whole thing is a "date")?
- how many ways can it be done (it can be done an infinite number of "times" with the same day/month)?

Assuming the above, I get:
18 (1/4, 2/5, 3/6, 4/7, 5/8, 6/9, 7/10, 8/11, 9/12, 4/1, 5/2, 6/3, 7/4, 8/5, 9/6, 10/7, 11/8, 12/9)

Ur answer is correct........

but u have not considered the change in duration between 80 to 90 days...In that case, actual correct answer is 9.

It may be of some passing interest to you both that transposition errors are often divisible by 9.

Yes, you are right.

Transposition errors (in integers) are always divisible by 9.

That depends on whether or not duration is a signed quantity...