Difference between revisions of "1990 AHSME Problems/Problem 10"

Revision as of 02:50, 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?

$\text{(A) 69} \quad \text{(B) IDK} \quad \text{(C) Deez nuts} \quad \text{(D) 9 +10 (21)} \quad \text{(E) (Not the answer)}$

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 $\fbox{D}$

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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Difference between revisions of "1990 AHSME Problems/Problem 10"

Revision as of 02:50, 14 February 2016

Problem

Solution

See also

@@ Line 12: / Line 12: @@
 <asy>import three;
 unitsize(1cm);size(100);
-draw((0,0,0)--(0,1,0),linewidth(2));
+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),linewidth(2));
+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),linewidth(2));
+draw((1,1,0)--(1,1,1),red);
 draw((0,1,1)--(1,1,1)--(1,0,1),red);
 </asy>