McNugget Numbers are any integer n which can be satisfied with the linear combination of 6a + 9b + 20c. Although it is known that all integers (with some exceptions*) are McNugget Numbers, it is still interesting to see how many possible linear combinations can be used to satisfy some n.

I’ve designed this small program to test if a number is potentially a McNugget Number. It will quickly sieve through if the number is able to satisfied with a x6 McNugget Box, a x9 McNugget Box or a x20 McNugget Box. Note that the program **doesn’t **consider all the possible ways of satisfying some integer n.

For example, 36 can be satisfied with {6,0,0}, {0,4,0} and {3,2,0}.

*As said earlier, the exception set of integers is the following: {1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, 43}, if we use the original box size set of {6, 9, 20}. I’ve ignored the newer {4,6,9,20} set of coefficients for the linear combination since this drastically reduces the number of non McNugget numbers to the set of {1, 2, 3, 5, 7, 11}.

The code is written in C++. The source file can download directly from here.

**References:**

McNugget Number – from Wolfram MathWorld

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## About 0x14c

I'm currently a Software Developer. My primary interests are Graph Theory, Number Theory, Programming Language Theory, Logic and Windows Debugging.