Difference between revisions of "2002 AIME II Problems/Problem 1"
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== Problem == | == Problem == | ||
− | + | Given that<br> | |
+ | <center><math>\begin{eqnarray*}&(1)& \text{x and y are both integers between 100 and 999, inclusive;}\qquad \qquad \qquad \qquad \qquad \\ | ||
+ | &(2)& \text{y is the number formed by reversing the digits of x; and}\\ | ||
+ | &(3)& z=|x-y|. \end{eqnarray*}</math></center> | ||
+ | How many distinct values of <math>z</math> are possible? | ||
== Solution == | == Solution == |
Revision as of 14:37, 9 August 2008
Problem
Given that
&(2)& \text{y is the number formed by reversing the digits of x; and}\\&(3)& z=|x-y|. \end{eqnarray*}$ (Error compiling LaTeX. ! Missing \endgroup inserted.)
How many distinct values of are possible?
Solution
We count the number of three-letter and three-digit palindromes, then subtract the number of license plates containing both types of palindrome.
There are letter palindromes, digit palindromes, and palindromes that contain both letters and digits.
Since there are possible plates, the probability desired is . Thus .
See also
2002 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |