On Sun, Aug 28, 2016 at 10:46 AM, shahan khan <shahankh...@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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