Difference between revisions of "2002 AIME II Problems/Problem 4"
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== Problem == | == Problem == | ||
| + | Patio blocks that are hexagons <math>1</math> unit on a side are used to outline a garden by placing the blocks edge to edge with <math>n</math> on each side. The diagram indicates the path of blocks around the garden when <math>n=5</math>. | ||
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| + | [[Image:AIME 2002 II Problem 4.gif]] | ||
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| + | If <math>n=202</math>, then the area of the garden enclosed by the path, not including the path itself, is <math>m\left(\sqrt3/2\right)</math> square units, where <math>m</math> is a positive integer. Find the remainder when <math>m</math> is divided by <math>1000</math>. | ||
== Solution == | == Solution == | ||
Revision as of 13:16, 19 April 2008
Problem
Patio blocks that are hexagons 
unit on a side are used to outline a garden by placing the blocks edge to edge with 
on each side. The diagram indicates the path of blocks around the garden when 
.
If 
, then the area of the garden enclosed by the path, not including the path itself, is 
square units, where 
is a positive integer. Find the remainder when is divided by 
.
Solution
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See also
| 2002 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
