Difference between revisions of "2013 AMC 8 Problems/Problem 22"
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Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether? | 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; | picture corner; | ||
draw(corner,(5,0)--(35,0)); | draw(corner,(5,0)--(35,0)); | ||
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draw((55,-100)--(85,-100),dotted+linewidth(2)); | draw((55,-100)--(85,-100),dotted+linewidth(2)); | ||
draw((50,-105)--(50,-135),dotted+linewidth(2)); | draw((50,-105)--(50,-135),dotted+linewidth(2)); | ||
| − | draw((0,-105)--(0,-135),dotted+linewidth(2)); | + | draw((0,-105)--(0,-135),dotted+linewidth(2));</asy> |
<math>\textbf{(A)}\ 1920 \qquad \textbf{(B)}\ 1952 \qquad \textbf{(C)}\ 1980 \qquad \textbf{(D)}\ 2013 \qquad \textbf{(E)}\ 3952</math> | <math>\textbf{(A)}\ 1920 \qquad \textbf{(B)}\ 1952 \qquad \textbf{(C)}\ 1980 \qquad \textbf{(D)}\ 2013 \qquad \textbf{(E)}\ 3952</math> | ||
Revision as of 18:27, 27 November 2013
Problem
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]](http://latex.artofproblemsolving.com/2/e/3/2e3ad97b03ca7e8f2c74a1ba60b45336d77a6756.png)
Solution
There are 
vertical columns with a length of 
toothpicks, and there are 
horizontal rows with a length of 
toothpicks. An effective way to verify this is to try a small case, i.e. a 
grid of toothpicks. Thus, our answer is 
.
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
