Difference between revisions of "2000 AMC 8 Problems/Problem 8"
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| − | - | + | ==Problem== |
| + | |||
| + | Three dice with faces numbered <math>1</math> through <math>6</math> are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is | ||
| + | |||
| + | <asy> | ||
| + | draw((0,0)--(2,0)--(3,1)--(3,7)--(1,7)--(0,6)--cycle); | ||
| + | draw((3,7)--(2,6)--(0,6)); | ||
| + | draw((3,5)--(2,4)--(0,4)); | ||
| + | draw((3,3)--(2,2)--(0,2)); | ||
| + | draw((2,0)--(2,6)); | ||
| + | |||
| + | dot((1,1)); dot((.5,.5)); dot((1.5,.5)); dot((1.5,1.5)); dot((.5,1.5)); | ||
| + | dot((2.5,1.5)); | ||
| + | dot((.5,2.5)); dot((1.5,2.5)); dot((1.5,3.5)); dot((.5,3.5)); | ||
| + | dot((2.25,2.75)); dot((2.5,3)); dot((2.75,3.25)); dot((2.25,3.75)); dot((2.5,4)); dot((2.75,4.25)); | ||
| + | dot((.5,5.5)); dot((1.5,4.5)); | ||
| + | dot((2.25,4.75)); dot((2.5,5.5)); dot((2.75,6.25)); | ||
| + | dot((1.5,6.5)); | ||
| + | </asy> | ||
| + | |||
| + | <math>\text{(A)}\ 21 \qquad \text{(B)}\ 22 \qquad \text{(C)}\ 31 \qquad \text{(D)}\ 41 \qquad \text{(E)}\ 53</math> | ||
==Solution== | ==Solution== | ||
Latest revision as of 06:57, 20 December 2024
Problem
Three dice with faces numbered 
through 
are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is
![[asy] draw((0,0)--(2,0)--(3,1)--(3,7)--(1,7)--(0,6)--cycle); draw((3,7)--(2,6)--(0,6)); draw((3,5)--(2,4)--(0,4)); draw((3,3)--(2,2)--(0,2)); draw((2,0)--(2,6)); dot((1,1)); dot((.5,.5)); dot((1.5,.5)); dot((1.5,1.5)); dot((.5,1.5)); dot((2.5,1.5)); dot((.5,2.5)); dot((1.5,2.5)); dot((1.5,3.5)); dot((.5,3.5)); dot((2.25,2.75)); dot((2.5,3)); dot((2.75,3.25)); dot((2.25,3.75)); dot((2.5,4)); dot((2.75,4.25)); dot((.5,5.5)); dot((1.5,4.5)); dot((2.25,4.75)); dot((2.5,5.5)); dot((2.75,6.25)); dot((1.5,6.5)); [/asy]](http://latex.artofproblemsolving.com/e/6/e/e6edba55d99924ea2b25e28f44f68200e0b47bed.png)
Solution
The numbers on one die total 
, so the numbers
on the three dice total 
. Numbers 
are visible, and these total 
.
This leaves 
not seen.
See Also
| 2000 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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. 
