Difference between revisions of "1998 AHSME Problems/Problem 29"

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== Solution ==
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== Solution 1 ==
 
Sadly, I don't actually have a solution. However, after doing some work on Geogebra, I have convinced myself that the answer is almost certainly A
 
Sadly, I don't actually have a solution. However, after doing some work on Geogebra, I have convinced myself that the answer is almost certainly A
 +
 +
 +
== Solution 2 ==
 +
Apply Pick's Theorem. 4 lattice points on the border edges, 3 points in the interior. <math>A = I + \frac{B}{2} -1</math>, implying that <math>max(A) = 4</math>, <math>\boxed{A}</math>
  
 
== See also ==
 
== See also ==
 
{{AHSME box|year=1998|num-b=28|num-a=30}}
 
{{AHSME box|year=1998|num-b=28|num-a=30}}

Revision as of 16:30, 18 February 2012

Problem

A point $(x,y)$ in the plane is called a lattice point if both $x$ and $y$ are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to

$\mathrm{(A) \ } 4.0 \qquad \mathrm{(B) \ } 4.2 \qquad \mathrm{(C) \ } 4.5 \qquad \mathrm{(D) \ } 5.0 \qquad \mathrm{(E) \ }  5.6$


Solution 1

Sadly, I don't actually have a solution. However, after doing some work on Geogebra, I have convinced myself that the answer is almost certainly A


Solution 2

Apply Pick's Theorem. 4 lattice points on the border edges, 3 points in the interior. $A = I + \frac{B}{2} -1$, implying that $max(A) = 4$, $\boxed{A}$

See also

1998 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 28
Followed by
Problem 30
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