Difference between revisions of "2021 JMPSC Sprint Problems/Problem 8"
(Created page with "==Problem== How many positive two-digit numbers exist such that the product of its digits is not zero? ==Solution== asdf") |
|||
| Line 3: | Line 3: | ||
==Solution== | ==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 <math>0</math>'s in their digits are the multiples of <math>10</math>. | ||
| + | |||
| + | <cmath>10, 20, 30, 40, 50, 60, 70, 80, 90</cmath> | ||
| + | |||
| + | Therefore, there are only <math>9</math> that satisfy the requirements. | ||
| + | |||
| + | -OofPirate | ||
Revision as of 00:21, 11 July 2021
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 
that satisfy the requirements.
-OofPirate
