Find the missing digits in this long division problem, where the division has no remainder, and other 7's...

arithmetic/digits/seven.sevens New, unsolved

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Find the missing digits in this long division problem, where the
division has no remainder, and other 7's can occur in the solution.

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

-- Barry Wolk <wolk@ccm.UManitoba.CA>

Show solution

No solution was found in the collected postings.

[ Editor: Barry Wolk posted this (first on Dec 9, 1994) as "a much
  harder problem of the same type" as the "burnt will" puzzle. ]

>  I have proofread this problem VERY carefully.

Well, anyone care to try to solve it this time? Problems involving long
division have so many clues that it is hard to know where to start.

-- Barry Wolk <wolk@ccm.UManitoba.CA>

Perhaps Barry knows this, but this problem is older than the 12-coins
puzzle.  It will celebrate its 90th birthday next year.  "Berwick's
Problem of the Seven Sevens" can be found reprinted in Heinrich D:orrie's
"100 Great Problems in Elementary Mathematics" as problem #4.  Note: he
takes 4 pages to solve it.

-- Wei-Hwa Huang (whuang@cco.caltech.edu), May 1995