Long Division Puzzle: Solving for Unknown Values Using Long Division Method

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Homework Help Overview

The discussion revolves around a long division puzzle involving unknown values represented by 'x'. Participants are tasked with interpreting a division statement where both the numerator and denominator contain these unknowns, and the quotient has a specific structure.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore whether the 'x' values are distinct digits or the same digit, questioning the implications of each interpretation on the division outcome.
  • There are discussions about the nature of remainders in division, particularly whether a remainder can exist when the numerator is less than the denominator.
  • Some participants suggest that the problem may have been misstated, leading to confusion about the correct interpretation of the division and the structure of the numbers involved.

Discussion Status

The conversation is ongoing, with various interpretations being explored. Some participants have attempted to provide examples and solutions, while others are questioning the validity of those examples and the original problem statement. There is no clear consensus on the correct approach or interpretation yet.

Contextual Notes

Participants note that the problem may involve constraints such as the leading digits not being zero and the nature of the remainder in relation to the divisor. There is also mention of the potential for infinite solutions depending on the interpretation of the digits.

Natasha1
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I found in this book the other day the following puzzle (but the book did not give any answer), if someone can do this could you explain, step by step proceedings please as I just get no where.

The question is this:

We are given the following division (each x is an unknown value)

xx / xxxxxxx = xx8xx

Hint: Think the long division way!
 
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Each "x" is the same exact digit? Then the answer would have to be less than 1, wouldn't it?
 
You mean each x is a distinct digit (not necessarily the same) ?

Surely, decimal points are permissible, but in that case the solutions must be infinite, or are all the x's the same digit ?
 
arunbg said:
You mean each x is a distinct digit (not necessarily the same) ?

Surely, decimal points are permissible, but in that case the solutions must be infinite, or are all the x's the same digit ?

Yes each x is a distinct digit (not necessarily the same). Yes I forgot to say sorry sorry!
There is a remainder of xxx (3 dictinct digits)
 
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Natasha1 said:
Yes each x is a distinct digit (not necessarily the same). Yes I forgot to say sorry sorry!
There is a remainder of xxx (3 dictinct digits)
How can xx / xxxxxxx have a remainder? The numerator has to be greater than the denominator for there to be a remainder, no?
 
berkeman said:
How can xx / xxxxxxx have a remainder? The numerator has to be greater than the denominator for there to be a remainder, no?

Sorry!

Of course it is:

xxxxxxx / xx = xx8xx with remainder of xxx
 
I think you're supposed to read it as divide xxxxxxx some 7 digit number (presumably the leading digits involved are never zero) by some two digit number. The quotient is 5 digits and the middle one is 8. Now, it doesn't make sense to say the remainder is three digits because the remainder on dividing by a 2 digit number is a one or 2 digit number.
 
Kinda' takes the fun out of the puzzle to have it misstated so many times, eh?
 
dead post - ignore me
 
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  • #10
3trQN said:
dead post - ignore me

well I managed to work it out anyway:

1089708 / 12 = 90809 with remainder of 108.

So there you go! :-)
 
  • #11
But 1089709 / 12 =90809 with a remainder of 109

exercise: find a load more examples...

Hint: start with any number, like 88888, now let's pick some two digit number, oh, like 88, what's 88*88888... it's 7822144, now add you favourite 3 digit number, like 100, and you've got another solution...

so, what ought to be the real statement of the problem?
 
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  • #12
Natasha1 said:
well I managed to work it out anyway:

1089708 / 12 = 90809 with remainder of 108.

So there you go! :-)
Inversion over your original post?

We are given the following division (each x is an unknown value)

xx / xxxxxxx = xx8xx

Hint: Think the long division way!
 
  • #13
matt grime said:
But 1089709 / 12 =90809 with a remainder of 109

exercise: find a load more examples...

Hint: start with any number, like 88888, now let's pick some two digit number, oh, like 88, what's 88*88888... it's 7822144, now add you favourite 3 digit number, like 100, and you've got another solution...

so, what ought to be the real statement of the problem?

Not sure MattGrime
 

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