Difference between revisions of "1998 AHSME Problems/Problem 29"
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| − | == Solution == | + | == 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 15:30, 18 February 2012
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
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. 
, implying that 
, 
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 | ||
