Henry Ernest Dudeney/Modern Puzzles/74 - Queer Division

by : $74$

 * Queer Division
 * ''The following is a rather curious puzzle in which we are restricted to the use of only $2$ digits.


 * Find the smallest number which when divided successively by $45$, $454$, $4545$, and $45454$
 * leaves the remainders $4$, $45$, $454$, and $4545$ respectively.


 * This is perhaps not very easy but it affords a good arithmetical exercise.