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

[Natasha1]

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!

 

[berkeman]

Each "x" is the same exact digit? Then the answer would have to be less than 1, wouldn't it?

 

[arunbg]

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 ?

 

[Natasha1]

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)

 

[berkeman]

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?

 

[Natasha1]

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

 

[matt grime]

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.

 

[berkeman]

Kinda' takes the fun out of the puzzle to have it misstated so many times, eh?

 

[3trQN]

dead post - ignore me

 

[Natasha1]

dead post - ignore me

well I managed to work it out anyway:

1089708 / 12 = 90809 with remainder of 108.

So there you go! :-)

 

[matt grime]

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?

 

[3trQN]

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!

 

[Natasha1]

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