Difference between revisions of "2012 AIME I Problems/Problem 11"
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==Problem 11== | ==Problem 11== | ||
| + | A frog begins at <math>P_0 = (0,0)</math> and makes a sequence of jumps according to the following rule: from <math>P_n = (x_n, y_n),</math> the frog jumps to <math>P_{n+1},</math> which may be any of the points <math>(x_n + 7, y_n + 2),</math> <math>(x_n + 2, y_n + 7),</math> <math>(x_n - 5, y_n - 10),</math> or <math>(x_n - 10, y_n - 5).</math> There are <math>M</math> points <math>(x, y)</math> with <math>|x| + |y| \le 100</math> that can be reached by a sequence of such jumps. Find the remainder when <math>M</math> is divided by <math>1000.</math> | ||
== Solution == | == Solution == | ||
Revision as of 00:27, 17 March 2012
Problem 11
A frog begins at 
and makes a sequence of jumps according to the following rule: from 
the frog jumps to 
which may be any of the points 
or 
There are 
points 
with 
that can be reached by a sequence of such jumps. Find the remainder when is divided by 
Solution
See also
| 2012 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 | ||
