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? | ||
+ | |||
<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> | + | 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> | + | </asy> |
− | \textbf{(A)}\ (C, A, E, D, B) \qquad | + | |
− | \textbf{(B)}\ (C, A, D, E, B) \qquad | + | <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>. | + | By careful inspection and common sense, the answer is <math>\textbf{(E)}</math>. |
− | + | == 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 == | == See also == | ||
Line 25: | Line 24: | ||
[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 15:43, 4 November 2023
Contents
Problem
There are coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
Solution
By careful inspection and common sense, the answer is .
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 (Problems • Answer Key • Resources) | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.