Difference between revisions of "2021 JMPSC Sprint Problems/Problem 8"
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| + | == Solution 2 == | ||
| + | You don't want a digit in this number to contain <math>0</math>. Therefore, the answer is <math>9 \cdot 9=\boxed{81}</math> | ||
| + | |||
| + | - kante314 - | ||
| + | |||
| + | ==See also== | ||
| + | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
| + | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
| + | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
| + | {{JMPSC Notice}} | ||
Latest revision as of 09:44, 12 July 2021
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 
.
![\[10, 20, 30, 40, 50, 60, 70, 80, 90\]](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
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. 
