Difference between revisions of "1987 AHSME Problems/Problem 16"

(Created page with "==Problem== A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base <math>5</math>. Second, a 1-to-1 correspondence...")
 
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\textbf{(C)}\ 82 \qquad
 
\textbf{(C)}\ 82 \qquad
 
\textbf{(D)}\ 108 \qquad
 
\textbf{(D)}\ 108 \qquad
\textbf{(E)}\ 113  </math>  
+
\textbf{(E)}\ 113  </math>
  
 
== See also ==
 
== See also ==

Revision as of 22:54, 3 June 2015

Problem

A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base $5$. Second, a 1-to-1 correspondence is established between the digits that appear in the expressions in base $5$ and the elements of the set $\{V, W, X, Y, Z\}$. Using this correspondence, the cryptographer finds that three consecutive integers in increasing order are coded as $VYZ, VYX, VVW$, respectively. What is the base-$10$ expression for the integer coded as $XYZ$?

$\textbf{(A)}\ 48 \qquad \textbf{(B)}\ 71 \qquad \textbf{(C)}\ 82 \qquad \textbf{(D)}\ 108 \qquad \textbf{(E)}\ 113$

See also

1987 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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