looping through possible combinations of McNuggets packs of 6, 9 and 20

[Ian Kelly]

On Sun, Aug 15, 2010 at 4:36 PM, Baba <raoulbia at gmail.com> wrote:
> Hi Mel,
>
> indeed i thought of generalising the theorem as follows:
> If it is possible to buy n, n+1,…, n+(x-1) sets of McNuggets, for some
> x, then it is possible to buy any number of McNuggets >= x, given that
> McNuggets come in x, y and z packs.
>
> so with diophantine_nuggets(7,10,21) i would need 7 passes
> result:53
>
> but with (10,20,30) and 10 passes i get no result

You're on the right track.  In the case of (10,20,30) there is no
largest exactly purchasable quantity.  Any quantity that does not end
with a 0 will not be exactly purchasable.

I suspect that there exists a largest unpurchasable quantity iff at
least two of the pack quantities are relatively prime, but I have made
no attempt to prove this.

Cheers,
Ian