MathDB
Colored Grid

Source:

January 1, 2009
geometryrectangle

Problem Statement

Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains 8 8 unit squares. The second ring contains 16 16 unit squares. If we continue this process, the number of unit squares in the 100th 100^\text{th} ring is <spanclass=latexbold>(A)</span> 396<spanclass=latexbold>(B)</span> 404<spanclass=latexbold>(C)</span> 800<spanclass=latexbold>(D)</span> 10, ⁣000<spanclass=latexbold>(E)</span> 10, ⁣404 <span class='latex-bold'>(A)</span>\ 396 \qquad <span class='latex-bold'>(B)</span>\ 404 \qquad <span class='latex-bold'>(C)</span>\ 800 \qquad <span class='latex-bold'>(D)</span>\ 10,\!000 \qquad <span class='latex-bold'>(E)</span>\ 10,\!404 [asy]unitsize(3mm);
defaultpen(linewidth(1pt));
fill((2,2)--(2,7)--(7,7)--(7,2)--cycle, mediumgray); fill((3,3)--(6,3)--(6,6)--(3,6)--cycle, gray); fill((4,4)--(5,4)--(5,5)--(4,5)--cycle, black);
for(real i=0; i<=9; ++i) { draw((i,0)--(i,9)); draw((0,i)--(9,i)); }[/asy]