1990 AHSME Problems/Problem 10

Revision as of 14:19, 2 April 2016 by Theboombox77 (talk | contribs) (Solution)

Problem

An $11\times 11\times 11$ wooden cube is formed by gluing together $11^3$ unit cubes. What is the greatest number of unit cubes that can be seen from a single point?

$\text{(A) 328} \quad \text{(B) 329} \quad \text{(C) 330} \quad \text{(D) 331} \quad \text{(E) 332}$

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] 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 331 or $\fbox{D}$

See also

1990 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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