# Supposedly Trivial math question.

S. Dale Morrey sdalemorrey at gmail.com
Tue Oct 1 14:45:29 MDT 2013

```The base is arbitrary, meaning if the customer is giving base 10 money then
all change must be base 10, i.e. 1's 10s, 100's etc.  As stated earlier
each bill is a power of the previous bill, there are no 0.25's or 20's or
other Americanisms to deal with.  What we would call 25 cents, would
optimally be handled (in base 10) with 2 tens and 5 ones, there would not
be a 25 coin bill.
Near the end he allowed me to just pick a base and lock my answer to that,
i.e. I no longer had to account for a different base.  So I included that
in the instructions upfront.

My solution (which I've only recently worked out), looks like this.

function makeChange(int base, int amountDue, int amountGiven){

changeDue = amountGiven - amountDue;
return breakBills(changeDue, base);
}

function breakBills(int amount,int base ){
static count x = 1;
dividend = floor(amount / base);
remainder = amount mod base;
if(remainder == 0){
return;
}else{
return dividend+"-" + (count * base) + "'s, " +
breakBills(remainder,base);
}

}

Theoretically this might be javascript, frankly it's out of thing air, I
haven't tested it yet, but it looks like it should work right?

}

On Tue, Oct 1, 2013 at 11:18 AM, Levi Pearson <levipearson at gmail.com> wrote:

> On Tue, Oct 1, 2013 at 11:10 AM, Richard Holden <rholdeniii at gmail.com>
> wrote:
> > Unless I'm reading it wrong it doesn't actually seem to require all of
> the
> > division. They say that the smallest fractional unit can be taken to be a
> > whole unit, so in the values stated the 123.45 and 1300.00 get changed to
> > whole units as 12345 integer and 130000 integer. That gives us the
> > calculation for the integer change as
> >
> >  130000
> > - 12345
> > -------
> >  117655
> >
> > To figure out the change we just convert the integer into a string
> > (assuming that the language of choice correctly converts) which should
> give
> > us "117655". If we reverse the string ("556711") and iterate over the
> > characters then the index becomes the power to which we raise the base.
> > i.e. pulling out the second 5 (index value 1) we could output 5-(10^1)s
> or
> > 5-10s, etc. Giving "5-1s 5-10s 6-100s 7-1000s 1-10000s 1-100000s"
> >
> > To do this in base 2 it just becomes
> > 5-(2^0)s 5-(2^1)s 6-(2^2)s 7-(2^3)s 1-(2^4)s 1-(2^5)s
> >
>
> This is true, and is usable if you get the input in the form of a
> string in the correct base.  If you get it as a number, either you or
> a library function would have to do the divisions in order to convert
> the number to a string in the correct base in the first place.  If
> that's the case, there's no point in using a string; you might as well
> use an array of digit values with the index as the power to which
> you'll raise the base before multiplying.  The problem definition is
> underspecified with respect to input/output, so it's not clear whether
> this approach is valid or not, but it's certainly sound if it is
> applicable.
>
>         --Levi
>
> /*
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>
```