Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 7"
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== Problem == | == Problem == | ||
| + | A coin of radius <math>1</math> is flipped onto an <math>500 \times 500</math> square grid divided into <math>2500</math> equal squares. Circles are inscribed in <math>n</math> of these <math>2500</math> squares. Let <math>P_n</math> be the probability that, given that the coin lands completely within one of the smaller squares, it also lands completely within one of the circles. Let <math>P</math> be the probability that, when flipped onto the grid, the coin lands completely within one of the smaller squares. Let <math>n_0</math> smallest value of <math>n</math> such that <math>P_n > P</math>. Find the value of <math>\left\lfloor \frac{n_0}{3} \right\rfloor</math>. | ||
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| + | == Solution == | ||
== Solution == | == Solution == | ||
Latest revision as of 20:18, 8 October 2014
Contents
Problem
A coin of radius 
is flipped onto an 
square grid divided into 
equal squares. Circles are inscribed in 
of these squares. Let 
be the probability that, given that the coin lands completely within one of the smaller squares, it also lands completely within one of the circles. Let 
be the probability that, when flipped onto the grid, the coin lands completely within one of the smaller squares. Let 
smallest value of such that 
. Find the value of 
.
Solution
Solution
See also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
