MathDB
2013/8/22/Toothpicks in a grid

Source:

November 27, 2013
AMC

Problem Statement

Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?
[asy] picture corner; draw(corner,(5,0)--(35,0)); draw(corner,(0,-5)--(0,-35)); for (int i=0; i<3; ++i) { for (int j=0; j>-2; --j) { if ((i-j)<3) { add(corner,(50i,50j)); } } } draw((5,-100)--(45,-100)); draw((155,0)--(185,0),dotted+linewidth(2)); draw((105,-50)--(135,-50),dotted+linewidth(2)); draw((100,-55)--(100,-85),dotted+linewidth(2)); draw((55,-100)--(85,-100),dotted+linewidth(2)); draw((50,-105)--(50,-135),dotted+linewidth(2)); draw((0,-105)--(0,-135),dotted+linewidth(2));[/asy]
<spanclass=latexbold>(A)</span> 1920<spanclass=latexbold>(B)</span> 1952<spanclass=latexbold>(C)</span> 1980<spanclass=latexbold>(D)</span> 2013<spanclass=latexbold>(E)</span> 3932<span class='latex-bold'>(A)</span>\ 1920 \qquad <span class='latex-bold'>(B)</span>\ 1952 \qquad <span class='latex-bold'>(C)</span>\ 1980 \qquad <span class='latex-bold'>(D)</span>\ 2013 \qquad <span class='latex-bold'>(E)</span>\ 3932