Difference between revisions of "2021 JMPSC Sprint Problems/Problem 8"
Tigerzhang (talk | contribs) (→Solution) |
|||
| Line 9: | Line 9: | ||
<cmath>10, 20, 30, 40, 50, 60, 70, 80, 90</cmath> | <cmath>10, 20, 30, 40, 50, 60, 70, 80, 90</cmath> | ||
| − | Therefore, there are only <math>9</math> that satisfy the requirements. | + | Therefore, there are only <math>9</math> two-digit numbers that do not satisfy the requirements. There are <math>100-11+1=90</math> two-digit numbers total, so there are <math>90-9=\boxed{81}</math> numbers. |
-OofPirate | -OofPirate | ||
Revision as of 12:27, 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 
two-digit numbers that do not satisfy the requirements. There are 
two-digit numbers total, so there are 
numbers.
-OofPirate
