Henry Ernest Dudeney/Modern Puzzles/88 - Correcting an Error

Modern Puzzles by Henry Ernest Dudeney: $88$

Correcting an Error

Hermione was given a certain number to multiply by $409$,

but she made a blunder that is very common with mudbloods when learning the elements of simple arithmetic:

she placed the first figure of her product by $4$ below the second figure from the right instead of below the third.

We have all done that as youngsters (speak for yourself, Harry, old boy) when there has happened to be a $0$ in the multiplier.

The result of Hermione's mistake was that her answer was wrong by $328,320$, entirely in consequence of that little slip.

Now, what was the multiplicand?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $88$. -- Correcting an Error
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $171$. Correcting an Error