Difference between revisions of "2011 AMC 12A Problems/Problem 2"

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== Problem ==
 
== Problem ==
 
There are <math>5</math> coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
 
There are <math>5</math> coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
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<asy>
 
<asy>
 
size(100); defaultpen(linewidth(.8pt)+fontsize(8pt));
 
size(100); defaultpen(linewidth(.8pt)+fontsize(8pt));
Line 8: Line 9:
 
draw(arc((-.588,-.809), 1.2, 75, 300));
 
draw(arc((-.588,-.809), 1.2, 75, 300));
 
draw(arc((-.951,.309), 1.2, 96, 228));
 
draw(arc((-.951,.309), 1.2, 96, 228));
label("$A$",(0,1),NW); label("$B$",(-1.1,.309),NW); label("$C$",(.951,.309),E); label("$D$",(-.588,-.809),W); label("$E$",(.588,-.809),S);</asy>
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label("$A$",(0,1),NW); label("$B$",(-1.1,.309),NW); label("$C$",(.951,.309),E); label("$D$",(-.588,-.809),W); label("$E$",(.588,-.809),S);
<math>
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</asy>
\textbf{(A)}\ (C, A, E, D, B) \qquad
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\textbf{(B)}\ (C, A, D, E, B) \qquad
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<math>\textbf{(A)}\ (C, A, E, D, B) \qquad \textbf{(B)}\ (C, A, D, E, B) \qquad \textbf{(C)}\ (C, D, E, A, B) \qquad \textbf{(D)}\ (C, E, A, D, B) \qquad \textbf{(E)}\ (C, E, D, A, B) </math>
\textbf{(C)}\ (C, D, E, A, B) \qquad
 
\textbf{(D)}\ (C, E, A, D, B) \qquad \\
 
\textbf{(E)}\ (C, E, D, A, B) </math>
 
  
 
== Solution ==
 
== Solution ==
By inspection, the answer is <math>\textbf{(E)}</math>.
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By careful inspection and common sense, the answer is <math>\textbf{(E)}</math>.
  
(rigor?)
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== Solution ==
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Note that this image is quite similar to a topological map. This means that the coin that appears closest to us is at the top and the coin that appears farthest from us is at the bottom.
  
 
== See also ==
 
== See also ==

Latest revision as of 15:43, 4 November 2023

Problem

There are $5$ coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

[asy] size(100); defaultpen(linewidth(.8pt)+fontsize(8pt)); draw(arc((0,1), 1.2, 25, 214)); draw(arc((.951,.309), 1.2, 0, 360)); draw(arc((.588,-.809), 1.2, 132, 370)); draw(arc((-.588,-.809), 1.2, 75, 300)); draw(arc((-.951,.309), 1.2, 96, 228)); label("$A$",(0,1),NW); label("$B$",(-1.1,.309),NW); label("$C$",(.951,.309),E); label("$D$",(-.588,-.809),W); label("$E$",(.588,-.809),S); [/asy]

$\textbf{(A)}\ (C, A, E, D, B) \qquad \textbf{(B)}\ (C, A, D, E, B) \qquad \textbf{(C)}\ (C, D, E, A, B) \qquad \textbf{(D)}\ (C, E, A, D, B) \qquad \textbf{(E)}\ (C, E, D, A, B)$

Solution

By careful inspection and common sense, the answer is $\textbf{(E)}$.

Solution

Note that this image is quite similar to a topological map. This means that the coin that appears closest to us is at the top and the coin that appears farthest from us is at the bottom.

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 AMC 12 Problems and Solutions

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