MathDB
The Killer Problem

Source: AMC 10B 2016 #14, AMC 12B 2016 #11

February 21, 2016
AMCAMC 10AMC 122016 AMC 12B2016 AMC 10BAMC 10 BAMC 12 B

Problem Statement

How many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line y=πxy=\pi x, the line y=0.1y=-0.1 and the line x=5.1?x=5.1?
<spanclass=latexbold>(A)</span> 30<spanclass=latexbold>(B)</span> 41<spanclass=latexbold>(C)</span> 45<spanclass=latexbold>(D)</span> 50<spanclass=latexbold>(E)</span> 57<span class='latex-bold'>(A)</span>\ 30 \qquad <span class='latex-bold'>(B)</span>\ 41 \qquad <span class='latex-bold'>(C)</span>\ 45 \qquad <span class='latex-bold'>(D)</span>\ 50 \qquad <span class='latex-bold'>(E)</span>\ 57