Henry Ernest Dudeney/Modern Puzzles/55 - The Repeated Quartette

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.

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