Difference between revisions of "2014 AIME I Problems/Problem 11"
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== Problem 11 == | == Problem 11 == | ||
| − | A token starts at the point <math>(0,0)</math> of an <math>xy</math>-coordinate grid and | + | A token starts at the point <math>(0,0)</math> of an <math>xy</math>-coordinate grid and then makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of <math>|y|=|x|</math> is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. |
== Solution == | == Solution == | ||
Revision as of 19:41, 14 March 2014
Problem 11
A token starts at the point 
of an 
-coordinate grid and then makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of 
is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See also
| 2014 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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. 
