Difference between revisions of "1990 AHSME Problems/Problem 10"
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An <math>11\times 11\times 11</math> wooden cube is formed by gluing together <math>11^3</math> unit cubes. What is the greatest number of unit cubes that can be seen from a single point? | An <math>11\times 11\times 11</math> wooden cube is formed by gluing together <math>11^3</math> unit cubes. What is the greatest number of unit cubes that can be seen from a single point? | ||
| − | <math>\text{(A) | + | <math>\text{(A) 328} \quad |
| − | \text{(B) | + | \text{(B) 329} \quad |
| − | \text{(C) | + | \text{(C) 330} \quad |
| − | \text{(D) | + | \text{(D) 331} \quad |
| − | \text{(E) | + | \text{(E) 332} </math> |
== Solution == | == Solution == | ||
Revision as of 13:17, 2 April 2016
Problem
An 
wooden cube is formed by gluing together 
unit cubes. What is the greatest number of unit cubes that can be seen from a single point?
Solution
![[asy]import three; unitsize(1cm);size(100); draw((0,0,0)--(0,1,0),red); draw((0,0,1)--(0,0,0)--(1,0,0)--(1,0,1),red); draw((0,0,1)--(1,0,1),red); draw((0,0,1)--(0,1,1)--(0,1,0)--(1,1,0)--(1,0,0),red); draw((1,1,0)--(1,1,1),red); draw((0,1,1)--(1,1,1)--(1,0,1),red); [/asy]](http://latex.artofproblemsolving.com/7/f/1/7f14f925c508d3156122e3ba9c7c4581669707a1.png)
The best angle for cube viewing is centered on the corner. Meaning three of the six faces are visible. So therefore, the answer is just counting the number of cubes on the three faces. Which is 330 or 
See also
| 1990 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
