Difference between revisions of "1998 AHSME Problems/Problem 29"
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== Solution 2 == | == 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> | + | 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> (This is incorrect, because the vertices are not necessarily lattice points. The key idea is in fact to consider the lines on which the sides lie, and in fact not the vertices. |
== See also == | == See also == | ||
{{AHSME box|year=1998|num-b=28|num-a=30}} | {{AHSME box|year=1998|num-b=28|num-a=30}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 22:35, 7 December 2014
Contents
Problem
A point 
in the plane is called a lattice point if both 
and 
are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to
Solution 1
The answer is actually (D)
Solution 2
Apply Pick's Theorem. 4 lattice points on the border edges, 3 points in the interior. 
, implying that 
, 
(This is incorrect, because the vertices are not necessarily lattice points. The key idea is in fact to consider the lines on which the sides lie, and in fact not the vertices.
See also
| 1998 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
