[Tutor] Problem

[Joel Goldstick]

On Sun, Aug 28, 2016 at 10:46 AM, shahan khan <shahankhan0 at gmail.com> wrote:
> Hello
> I'm teching myself Python using MIT opencourse ware. I'm a beginner and
> have some what knowledge of c and c++. I'm using Python version
>
> Here is the problem:
> McDiophantine: Selling McNuggets
> In mathematics, a Diophantine equation (named for Diophantus of Alexandria,
> a third century Greek mathematician) is a polynomial equation where the
> variables can only take on integer values. Although you may not realize it,
> you have seen Diophantine equations before: one of the most famous
> Diophantine equations is:
> xn + yn= zn.
> For n=2, there are infinitely many solutions (values for x, y and z) called
> the Pythagorean triples, e.g. 32 + 42 = 52. For larger values of n,
> Fermat’s famous “last theorem” states that there do not exist any positive
> integer solutions for x, y and z that satisfy this equation. For centuries,
> mathematicians have studied different Diophantine equations; besides
> Fermat’s last theorem, some famous ones include Pell’s equation, and the
> Erdos-Strauss conjecture. For more information on this intriguing branch of
> mathematics, you may find the Wikipedia article of interest.
> We are not certain that McDonald’s knows about Diophantine equations
> (actually we doubt that they do), but they use them! McDonald’s sells
> Chicken McNuggets in packages of 6, 9 or 20 McNuggets. Thus, it is
> possible, for example, to buy exactly 15 McNuggets (with one package of 6
> and a second package of 9), but it is not possible to buy exactly 16
> nuggets, since no non-negative integer combination of 6’s, 9’s and 20’s
> adds up to 16. To determine if it is possible to buy exactly n McNuggets,
> one has to solve a Diophantine equation: find non-negative integer values
> of a, b, and c, such that
> 6a + 9b + 20c = n.
> Problem 1.
> Show that it is possible to buy exactly 50, 51, 52, 53, 54, and 55
> McNuggets, by finding solutions to the Diophantine equation. You can solve
> this in your head, using paper and pencil, or writing a program. However
> you chose to solve this problem, list the combinations of 6, 9 and 20 packs
> of McNuggets you need to buy in order to get each of the exact amounts.
> Given that it is possible to buy sets of 50, 51, 52, 53, 54 or 55 McNuggets
> by combinations of 6, 9 and 20 packs, show that it is possible to buy 56,
> 57,…, 65 McNuggets. In other words, show how, given solutions for 50-55,
> one can derive solutions for 56-65.
> Theorem: If it is possible to buy x, x+1,…, x+5 sets of McNuggets, for some
> x, then it is possible to buy any number of McNuggets >= x, given that
> McNuggets come in 6, 9 and 20 packs.
>
> Here is my code:
>  for a in range(1,10):
> for b in range(1,5):
> for c in range(1,5):
> mc=(6*a)+(9*b)+(20*c)
> if mc==50:
> print a,b,c
> else:
> print a,b,c
> a=+1
> b=b+1
> c=c+1

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