Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "How many times does the digit 9 appear in the list of all integers from 1 to 500? (The number $ 99 $, for example, is counted twice, because $9$ appears two times in it.)"
Line 1: Line 1:
−
{{delete|Although this is a mathematics problem, the title is unbelievably long. You may want to delete this.}}
 
  
−
How many times does the digit 9 appear in the list of all integers from 1 to 500? (The number <math> 99 </math>, for example, is counted twice, because <math>9</math> appears two times in it.)
 
−
The answer is.....
 
  
  
 
The easiest approach is to consider how many times 9 can appear in the units place, how many times in the tens place, and how many times in the hundreds place. If we put a 9 in the units place, there are 10 choices for the tens place and 5 choices for the hundreds digit (including 0), for a total of 50 times. Likewise, if we put a 9 in the tens place, there are 10 choices for the units place and 5 choices for the hundreds digit, for a total of 50 times. Since 9 cannot appear in the hundreds digit, there are <math>50+50=\boxed{100}</math> appearances of the digit 9.
 
The easiest approach is to consider how many times 9 can appear in the units place, how many times in the tens place, and how many times in the hundreds place. If we put a 9 in the units place, there are 10 choices for the tens place and 5 choices for the hundreds digit (including 0), for a total of 50 times. Likewise, if we put a 9 in the tens place, there are 10 choices for the units place and 5 choices for the hundreds digit, for a total of 50 times. Since 9 cannot appear in the hundreds digit, there are <math>50+50=\boxed{100}</math> appearances of the digit 9.

Revision as of 23:05, 24 January 2021


The easiest approach is to consider how many times 9 can appear in the units place, how many times in the tens place, and how many times in the hundreds place. If we put a 9 in the units place, there are 10 choices for the tens place and 5 choices for the hundreds digit (including 0), for a total of 50 times. Likewise, if we put a 9 in the tens place, there are 10 choices for the units place and 5 choices for the hundreds digit, for a total of 50 times. Since 9 cannot appear in the hundreds digit, there are $50+50=\boxed{100}$ appearances of the digit 9.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=How_many_times_does_the_digit_9_appear_in_the_list_of_all_integers_from_1_to_500%3F_(The_number_$_99_$,_for_example,_is_counted_twice,_because_$9$_appears_two_times_in_it.)&oldid=143214"