"Since the Happy MealTM-sized nugget box (4 to a box) can now be purchased separately, the modern McNugget numbers are linear combinations of 4, 6, 9, and 20." - http://mathworld.wolfram.com/McNuggetNumber.html

Question

usukidoll · Answer

yeah and I would like the Big Mac sauce with my McNuggets Please.

ganeshie8 · Answer

only addition is allowed right ?

ganeshie8 · Answer

The linear combinations of 9 and 20 actually generate all the integers

ganeshie8 · Answer

$$9x + 20y =n$$
has infinitely many "integer" solutions for every integer $n$

ganeshie8 · Answer

But since negative McNuggets make no sense, I think subtraction should not be allowed in the linear combs

empty · Answer

Yeah, I think you can't order negative McNuggets haha, this whole thing is making me giggle but it is interesting in and of itself haha. I think I've heard of these before a long time ago.

ganeshie8 · Answer

$$6x+9y+20z=n$$

over nonegative integers

empty · Answer

That is quite peculiar to me how you can sort of partially factor it inside as either:

$$3(2x+3y)+20z  = 2(3x+10z)+9y$$

ganeshie8 · Answer

Yeah this is analogous to the coin problem : 
$$5n+10d+25q = n$$

number of cents $n$ that can be made using nickels, dimes, and quarters

ganeshie8 · Answer

this coin problem is easy to solve :

since $\gcd(5,10,25)=5$, 
 $n$ must be a multiple of $5$.

So, we can make only multiples of 5 using nickels, dimes, and quarters... not very interesting..