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

(Solution 1)
(Solutions 1 and 2)
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We find that the 85th combination ends with the letter S.  
 
We find that the 85th combination ends with the letter S.  
 
So the answer is <math>\textbf{(C)}\ S</math>.
 
So the answer is <math>\textbf{(C)}\ S</math>.
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==Solution 2==
  
 
== See also ==
 
== See also ==

Revision as of 16:17, 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 $\textbf{(C)}\ S$.

Solution 2

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
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