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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?
  
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<math>\text{(A) 69} \quad
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<math>\text{(A) (Answer choices were lost)} \quad
−
\text{(B) IDK} \quad
+
\text{(B) (Answer choices were lost)} \quad
−
\text{(C) Deez nuts} \quad
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\text{(C) (Answer choices were lost)} \quad
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\text{(D) 9 +10 (21)} \quad
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\text{(D) 330} \quad
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\text{(E) (Not the answer)} </math>
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\text{(E) (Answer choices were lost)} </math>
  
 
== Solution ==
 
== Solution ==

Revision as of 02:52, 14 February 2016

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?

$\text{(A) (Answer choices were lost)} \quad \text{(B) (Answer choices were lost)} \quad \text{(C) (Answer choices were lost)} \quad \text{(D) 330} \quad \text{(E) (Answer choices were lost)}$

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 330 or $\fbox{D}$

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

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