Difference between revisions of "1986 AHSME Problems/Problem 10"

(Created page with "==Problem== The <math>120</math> permutations of the <math>AHSME</math> are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the <m...")
 
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\textbf{(E)}\ \text{E}  </math>   
 
\textbf{(E)}\ \text{E}  </math>   
  
==Solution==
+
==Solution 1==
  
 +
We could list out all of the possible combinations in dictionary order.
 +
 +
<math>73rd:</math> MAEHS                 
 +
<math>74th:</math> MAESH
 +
<math>75th:</math> MAHES
 +
<math>76th:</math> MAHSE
 +
<math>77th:</math> MASEH
 +
<math>78th:</math> MASHE
 +
<math>79th:</math> MEAHS
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<math>80th:</math> MEASH
 +
<math>81th:</math> MEHAS
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<math>82th:</math> MEHSA
 +
<math>83th:</math> MESAH
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<math>84th:</math> MESHA
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<math>85th:</math> MHAES
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We find that the 85th combination ends with the letter S.
 +
So the answer is <math>\textbf{(C)}\ S</math>.
  
 
== See also ==
 
== See also ==

Revision as of 15:16, 24 February 2016

Problem

The $120$ permutations of the $AHSME$ are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the $85$th word in this list is:

$\textbf{(A)}\ \text{A} \qquad \textbf{(B)}\ \text{H} \qquad \textbf{(C)}\ \text{S} \qquad \textbf{(D)}\ \text{M}\qquad \textbf{(E)}\ \text{E}$

Solution 1

We could list out all of the possible combinations in dictionary order.

$73rd:$ MAEHS $74th:$ MAESH $75th:$ MAHES $76th:$ MAHSE $77th:$ MASEH $78th:$ MASHE $79th:$ MEAHS $80th:$ MEASH $81th:$ MEHAS $82th:$ MEHSA $83th:$ MESAH $84th:$ MESHA $85th:$ MHAES

We find that the 85th combination ends with the letter S. So the answer is $\textbf{(C)}\ S$.

See also

1986 AHSME (ProblemsAnswer KeyResources)
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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