Henry Ernest Dudeney/Modern Puzzles/55 - The Repeated Quartette
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Modern Puzzles by Henry Ernest Dudeney: $55$
- The Repeated Quartette
- If we multiply $64253$ by $365$ we get the product $23452345$, where the first $4$ figures are repeated.
- What is the largest number that we can multiply by $365$ in order to produce a similar product of $8$ figures repeated in the same order?
- There is no objection to a repetition of figures -- that is, the $4$ that are repeated need not be all different, as in the case shown.
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Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $55$. -- The Repeated Quartette
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $106$. The Repeated Quartette