# 2021 JMPSC Sprint Problems/Problem 8

## Contents

## 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 .

Therefore, there are only two-digit numbers that do not satisfy the requirements. There are two-digit numbers total, so there are numbers.

-OofPirate

## Solution 2

You don't want a digit in this number to contain . Therefore, the answer is

- kante314 -

## See also

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.