Difference between revisions of "2013 AIME I Problems/Problem 2"
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−  == Problem  +  == Problem == 
Find the number of fivedigit positive integers, <math>n</math>, that satisfy the following conditions:  Find the number of fivedigit positive integers, <math>n</math>, that satisfy the following conditions:  
Latest revision as of 19:03, 24 January 2021
Contents
Problem
Find the number of fivedigit positive integers, , that satisfy the following conditions:

(a) the number is divisible by

(b) the first and last digits of are equal, and

(c) the sum of the digits of is divisible by
Solution
The number takes a form of , in which . Let and be arbitrary digits. For each pair of , there are exactly two values of that satisfy the condition of . Therefore, the answer is
Video Solution
https://www.youtube.com/watch?v=kz3ZX4PT_0 ~Shreyas S
See also
2013 AIME I (Problems • Answer Key • Resources)  
Preceded by Problem 1 
Followed by Problem 3  
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15  
All AIME Problems and Solutions 
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.