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

[Roald de Vries]

On Aug 13, 2010, at 12:25 PM, Roald de Vries wrote:
> My previous algorithm was more efficient, but for those who like one- 
> liners:
>
> [x for x in range(120) if any(20*a+9*b+6*c == x for a in range(x/20)  
> for b in range(x/9) for c in range(x/6))][-1]

OK, I did some real testing now, and there's some small error in the  
above. All solutions for all x's are given by:

     [(x, a, b, c) for x in range(120) for a in range(x/20+1) for b in  
range(x/9+1) for c in range(x/6+1) if x == a*20+b*9+c*6]

... and all non-solutions by:

     [x for x in range(120) if not any(x == a*20+b*9+c*6 for a in  
range(x/20+1) for b in range(x/9+1) for c in range(x/6+1))]

Cheers, Roald