Hundred Fowls

Solutions to the "Hundred Fowl" puzzle.

I'd fool around with pen and paper for a while, maybe days, until I found the solution.
Well I might have chosen this method in my pre-teens before I discovered a wonderful book on Number Theory in the Arncliffe Branch of the Rockdale Municipal Library. I wore that puppy out. B
I'd write a Perl/Python script.
My recent scribblings at 2am in hospital on pain killers would be shorter and quicker to produce. Correct as well. I'd also not accept the solution with one-third of a chicken. F
I'd use some math I learned at school, maybe consulting a book.
Ahh! Send a résumé. A+
I don't know how to do this.
Honest. You might like to read a book on Number Theory. A good programmer you might become one day. B+
I used Mathematica.
OK. Skip the class, go to the pub (I won't nit-pick, pocket calculators were allowed). Like this?

Reduce[{c >= 0, h >= 0, k >= 0, 5 c + 3 h + k/3 == 100, c + h + k == 100}, {c, h, k}, Integers]

(Answer elided.)

Extra credit: f(10) = 434460632656258183416749, f(9) = 5975780706516831163205. What are f(11) and f(8)?
Hint: they are cool but but not exactly spectacular integers - call our 1-900 number for f(1).

No - I won't give the numeric chook solutions. I encourage you to solve it. A free chunder.com postcard to the first and any funny solutions, which may be presented here with your permission.