Problem 1130

Solution One (Adjustment Method) First, prove that all candies can be concentrated in 2 or 3 plates after a finite number of operations.

In fact, if the number of plates with candies is no less than 3, take any 3 of them, denoted as $A, B, C$, and assume that $A, B, C$ contain $a, b, c (0 < b > c \geqslant 0$ respectively. This can be divided into the following two cases:
(1) If $a=c+2$, then $b=c+1$, since $a+b+c=3c+3 \geqslant 4$, so $c \geqslant 1$. Thus, the following steps can be performed to concentrate all candies in one plate after a finite number of operations:
$$(c+2, c+1, c, 0) \rightarrow(c+1, c, c, 2) \rightarrow(c, c+2, c, 1) \rightarrow(c-1, c+2, c+2,0) \rightarrow{ }^{c+2}+$$
$\rightarrow(3c+3,0,0,0)$.
(2) If $a>c+2$, then first perform the following operation on plates $A, B, C$:
$$(a, b, c) \rightarrow(a-1, b-1, c+2) \text{. }$$

Since $a>b>c$ and $a>c+2$, it follows that $a-1>b-1 \geqslant c, a-1 \geqslant(c+3)-1=c+2$, so after adjustment, the maximum number of candies in the three plates decreases by 1, while the minimum number does not decrease. Therefore, after a finite number of adjustments, it can be reduced to the case where the number of candies in two plates is equal or to the aforementioned case (1). Thus, according to the previous proof, all candies can be concentrated in one plate after a finite number of operations.