# Seven sevens cryptarithmetic

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

• Please quote the book you used as a source Oct 2, 2020 at 17:09
• 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. Jul 26, 2023 at 23:33
• @HemantAgarwal google.co.kr/books/edition/… Jul 26, 2023 at 23:54
• Thanks..any idea where one can buy the ebook in English ? Do you know if an English version exists ? Jul 26, 2023 at 23:57
• @HemantAgarwal I don't think it's been translated to English, sorry. Jul 27, 2023 at 0:00

## 1 Answer

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).

• Not showing your work just because there was a lot of it isn't how we do things around here.
– Bass
Oct 3, 2020 at 6:56
• @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. Oct 3, 2020 at 11:49