Question 16
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 $XYZ?$