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# Missing digits in long division

Posted on 2003-03-07
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I have posted a arithmetical restoration problem in the 'Puzzles and Riddles' section under the title 'Missing digits in long division' if anyone would like to have a go. - George
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Question by:duz
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ID: 8089858
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:)    good idea (the link)                 (so why is this one 50 pt?)
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:-D I have my moments
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duz,
I this is a 3 digit number xxx dividing into an 8 digit number xxxxxx with no remainder then it can not be done since xxxxxxxx/xxx = 100100.0991  for all x (easily proved). So either there is no solution or there must be a remainder to this problem or x possibly represents 2 or more digits.

Gwynforweb

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I meant "If this is a 3 digit number xxx dividing into an 8 digit number xxxxxxxx"
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duz

xxxxxxxx/xxx=(x*11111111)(x*111)=11111111/111=100100.0991

ie xxx does not divide xxxxxxxx for any x, 0 < x <=9

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Gwyn - not sure - but I think all of the differant x's = differant numerals.

not 33333333/333 - more like 34985124/342

btw everybody not the answer (as far as I know)- random typing above.

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> 11111111/111=100100.0991

?

> differant x's = differant numerals.

ditto that, consider swapping the X's with #'s if that helps.

btw, if you missed it, I think this will be initial format of problem, but it is not necessary except for context.

> :-D I have my moments

ditto
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Accepted Solution

SunBow earned 200 total points
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meintsi> 10,007,916 / 124 = 80709
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More complete for all the missing digits of formatted problem (adding vertical bars to identify interim remainders and dividend pull-downs):

YYYYYYY8|0709
YYYY--------
124\1000|7916
YYYYY992|                     - four digits from dividend
YYYY------
YYYYYYY8|79                 ; remainder is single digit
YYYYYYY8|68                   - two more digits from dividend
YYYYYYY-----
YYYYYYYY11|16              ; remainder is two digits
YYYYYYYY11|16                - two more digits from dividend
YYYYYYYY----
YYYYYYYYYYY|0              ; remainder = 0 (final)
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thedevilinthebelfry/SunBow Thanks , now I understand, sorry a bit slow today
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I think this is joke question ie xxxxxxxx=xx7xx*xxx
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eg 81706=10049838/123
91702=11371048/124
66766=14822052/222
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Thanks SunBow - it did my head in as well :-)
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You are welcome, and, thanx also for 'E' for effort. Nice problem.

-[ Good Fortune ]-
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> it did my head in as well :-)

In my head? I'd have been tempted to 1st program all possibles, or even Excel it, but for the overt hint of trick needing a clue. More power to ya, for me half of such effort is doing the columns, and by blowing one initially, I began to fill my head with some false assumptions. Overall though, it was nice, went rather well with up to, what, a half dozen participants? Good job.
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Way to go SUNBOW...................
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I thank you very kindly for that ........                                   -[Good Fortune]-
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Xxxxxxxx divided by xxx with answer x7x0x
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