2021 JMPSC Sprint Problems/Problem 8
Problem
How many positive two-digit numbers exist such that the product of its digits is not zero?
Solution
Rather than counting all the two-digit numbers that exist with those characteristics, we should do complementary counting to find the numbers with the product of its digits as 0.
The only numbers with 
's in their digits are the multiples of 
.
![\[10, 20, 30, 40, 50, 60, 70, 80, 90\]](http://latex.artofproblemsolving.com/6/b/c/6bc985146e83c8037f360d098d036818d0ace93c.png)
Therefore, there are only 
two-digit numbers that do not satisfy the requirements. There are 
two-digit numbers total, so there are 
numbers.
-OofPirate
