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This is not my original, but one of the older puzzles I found in an almost-20-years-old puzzle book1. It's definitely not the original of the book's author either, so I can't tell the real original source. When I encountered this for the first time, it took me a whole day to solve to the end.

Complete the following long division. An asterisk may contain any single digit from 0 to 9, except that leading zeros are not permitted.

                        * * 7 * *
            ---------------------
* * * * 7 * ) * * 7 * * * * * * *
              * * * * * *
              -------------------
              * * * * * 7 *
              * * * * * * *
              -------------------
                  * 7 * * * *
                  * 7 * * * *
                  ---------------
                  * * * * * * *
                  * * * * 7 * *
                  ---------------
                      * * * * * *
                      * * * * * *
                      -----------
                                0

1 Fun Math Puzzles for Genius (Korean), Boo-sung Park, 2001

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    $\begingroup$ Please quote the book you used as a source $\endgroup$
    – Dr Xorile
    Oct 2, 2020 at 17:09
  • $\begingroup$ Can you provide an Amazon or Google books link of the book ? Some other link will also do. I can neither find the author nor the book online. $\endgroup$ Jul 26, 2023 at 23:33
  • $\begingroup$ @HemantAgarwal google.co.kr/books/edition/… $\endgroup$
    – Bubbler
    Jul 26, 2023 at 23:54
  • $\begingroup$ Thanks..any idea where one can buy the ebook in English ? Do you know if an English version exists ? $\endgroup$ Jul 26, 2023 at 23:57
  • $\begingroup$ @HemantAgarwal I don't think it's been translated to English, sorry. $\endgroup$
    – Bubbler
    Jul 27, 2023 at 0:00

1 Answer 1

4
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It is

$7375428413 \div 125473 = 58781$.

I started by noticing that

$7$ times the divisor is still $6$-digit, so the divisor is at most $142857$; but other two digits times the divisor both become $7$-digit, so they must be $8$ or $9$.

and got the answer with some more efforts (which is too lengthy to write down).

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    $\begingroup$ Not showing your work just because there was a lot of it isn't how we do things around here. $\endgroup$
    – Bass
    Oct 3, 2020 at 6:56
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    $\begingroup$ @Bass I apologise for the low quality of my answer. However, I'm not going to update it, as I would rather spend the time doing more creative things. For me, the reward of solving the puzzle is the puzzle itself. Please feel free to post your higher quality answer. $\endgroup$
    – WhatsUp
    Oct 3, 2020 at 11:49

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