Still the best...

[Kevin O'Gorman]

On Sun, Jun 23, 2002 at 07:10:52AM -0500, David A. Bandel wrote:
> On Sat, 22 Jun 2002 18:51:06 -0700
> begin  "Kevin O'Gorman" <kevin at kosmanor.com> spewed forth:
> 
> [snip]
> 
> > In fact, I calculate (this the help of my local friendly Linux machine)
> > that there are exactly 240 ways to do it.  It's very simple to do; just
> > try 0-4 quarters, then 0 to some number of dimes (depending on how many
> > quarters), 0 to some number of nickels, and pennies to fill out the
> > buck. Here's what it looks like in Python:
> > 
> > #!/usr/bin/python
> > w = 0
> > for q in range(0,5):
> >     for d in range(0,10):
> >         if q*25+d*10>100: break
> >         for n in range (0,20):
> >             if q*25 + d*10 + n*5 > 100: break
> >             w = w + 1
> >             print \
> >    "%2.2d quarters, %2.2d dimes, %2.2d nickels, %3.3d pennies: %d ways"
> >    \
> >                % (q, d, n, 100- q*25 - d*10 - n*5, w)
> > 
> > 
> 
> Please grep your output for:
> 20 nickels
> 10 dimes
> and there?s a number of others missing.  Last time I looked, the above 2
> were legitimate ways to change a dollar.
> 
> Just by inspection, 240 cannot be the correct number.  The number will be
> odd.

Oops, you're right.  I don't use Python enough to rememeber reliably
that range() needs to overshoot.  I got it right for quarters, but forgot
the other two.  This however adds just two cases, the count is 242, still
less than 293, and even.

The new program is

> > #!/usr/bin/python
> > w = 0
> > for q in range(0,5):
> >     for d in range(0,11):
> >         if q*25+d*10>100: break
> >         for n in range (0,21):
> >             if q*25 + d*10 + n*5 > 100: break
> >             w = w + 1
> >             print \
> >    "%2.2d quarters, %2.2d dimes, %2.2d nickels, %3.3d pennies: %d ways" \
> >                % (q, d, n, 100- q*25 - d*10 - n*5, w)



++ kevin


-- 
Kevin O'Gorman  (805) 650-6274  mailto:kevin at kosmanor.com
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