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Problem set 2, problem 4

MIT 6.00 Intro Computer Science (OCW)
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I'm having trouble with problem four. For problem three, I exploited the fact that because the GCD of 6 and 9 is 3 and because 6 and 9 are three apart, any multiple of 3 > 6 is a buyable number of mcnuggets. And if the number is greater than 20, you can just subtract twenty and repeat that test. But for problem four, I'm trying to write a program that asks the user for the values of x, y, and z. Basically, it starts by asking you to set the values of the small, medium, and large sizes of mcnuggets, then proceeds to do the same test. At least, I'd like it to perform the same test. Can any advise me on a mathematical strategy/method for how solve a diophantine equation? I'm fine with doing an "exhaustive search" as the instructions say, basically looking at every possible combination of x, y, and z, but I can't figure our a way to represent that logically. Make sense?
I used a series of nested loops to test various quantities of smalls, mediums, and larges
The thing that I used to limit the loop was the total number of possible McNuggets--the problem says "find the largest number (less than 200) of McNuggets that cannot be bought in exact quantity," so if you get up to 200, you can stop. Then for me the relevant question became "If I can test total numbers of McNuggets up to a certain number, how can I test each possible combination of size-quantities that might total that number of McNuggets?"

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