2021 JMPSC Sprint Problems/Problem 8

Revision as of 01:21, 11 July 2021 by Oofpirate (talk | contribs)

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 $0$'s in their digits are the multiples of $10$.

\[10, 20, 30, 40, 50, 60, 70, 80, 90\]

Therefore, there are only $9$ that satisfy the requirements.

-OofPirate