Difference between revisions of "2013 AMC 8 Problems/Problem 22"
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==Problem== | ==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] | ||
| + | |||
| + | <math>\textbf{(A)}\ 1920 \qquad \textbf{(B)}\ 1952 \qquad \textbf{(C)}\ 1980 \qquad \textbf{(D)}\ 2013 \qquad \textbf{(E)}\ 3952</math> | ||
==Solution== | ==Solution== | ||
Revision as of 12:53, 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]
Solution
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
