@Darius4God ,
154 = 1 mod 3
101 = 2 mod 3
46 = 1 mod 3
22 = 1 mod 3
19 = 1 mod 3
17 = 2 mod 3
16 = 1 mod 3
13 = 1 mod 3
10 = 1 mod 3
Total = 398 = 2 mod 3
A + B + C = 398
2B + B + C = 398
3B + C = 398
C = 2 mod 3
Groups of 3 are going to be:
0 mod 3 (1 + 1 + 1),
1 mod 3 (1 + 1 + 2), or
2 mod 3 (1 + 2 + 2)
Since C = 2 mod 3, it must contain 101 and 17.
That leaves 154, 46, 22, 19, 16, 13, and 10.
Since A = 2B, 154 must be in A or C.
If 154 is in A, then A is at least 154+13+10 = 177 and B is at most 46+22+19=87.
Therefore, A is greater than twice B.
Therefore, 154 must be in C.
Therefore, C is 154+101+17 = 272.
No need to evaluate the C(9,3)*C(6,3)*C(3,3) = 1680 ways of distributing the nuggets among A, B, and C.