Henry Ernest Dudeney/Modern Puzzles/74 - Queer Division

Modern Puzzles by Henry Ernest Dudeney: $74$

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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $74$. -- Queer Division
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $121$. Queer Division