Difference between revisions of "1994 AIME Problems/Problem 6"

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== Problem ==
 
== Problem ==
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The graphs of the equations
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<center><math>y=k, \qquad y=\sqrt{3}x+2k, \qquad y=-\sqrt{3}x+2k,</math></center>
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are drawn in the coordinate plane for <math>k=-10,-9,-8,\ldots,9,10.\,</math>  These 63 lines cut part of the plane into equilateral triangles of side <math>2/\sqrt{3}.\,</math>  How many such triangles are formed?
  
 
== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}
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== See also ==
 
== See also ==
* [[1994 AIME Problems/Problem 5 | Previous problem]]
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{{AIME box|year=1994|num-b=5|num-a=7}}
* [[1994 AIME Problems/Problem 7 | Next problem]]
 
* [[1994 AIME Problems]]
 

Revision as of 22:28, 28 March 2007

Problem

The graphs of the equations

$y=k, \qquad y=\sqrt{3}x+2k, \qquad y=-\sqrt{3}x+2k,$

are drawn in the coordinate plane for $k=-10,-9,-8,\ldots,9,10.\,$ These 63 lines cut part of the plane into equilateral triangles of side $2/\sqrt{3}.\,$ How many such triangles are formed?

Solution

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See also

1994 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions
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