7. (10 points) Three positive integers greater than 1000 satisfy: the unit digit of the sum of any two of these numbers is equal to the unit digit of the third number. Then, the last three digits of the product of these 3 numbers have $\qquad$ possible values.
【Analysis】Assuming the units of the three numbers are $a$, $b$, and $c$, according to the condition "the units digit of the sum of any two numbers is equal to the units digit of the third number," the three numbers can be divided into three cases: (1) If $a$, $b$, and $c$ are all equal, then they can only all be $0$; (2) If two of $a$, $b$, and $c$ are equal; (3) If $a$, $b$, and $c$ are all different; solve accordingly.

【Solution】Solution: Let the units of the three numbers be $a$, $b$, and $c$.
(1) If $a$, $b$, and $c$ are all equal, then they can only all be 0;
(2) If two of $a$, $b$, and $c$ are equal, then there are the following two cases:
(1). $a$, $a$, $c$ and $a \neq c$, then $c + a = a$, $a + a = 10 + c$, then $a = 5$, $c = 0$;
(3). If $a$, $b$, and $c$ are all different, let $a < b < c$, then $c + b = 10 + a$, $c + a = 10 + b$, then $c = 10$, which contradicts $c$ being a digit;

In summary, the units of the three numbers are $0,0,0$ or $0,5,5$;
(1). If all are 0, then the last three digits of the product are 000;
(2). If they are $0,5,5$
(1). If the number with units 0 has the last three digits all 0, then the last three digits of the product are 000;
(2). If the number with units 0 has the last two digits all 0, then the last three digits of the product are 500 or 000;
(3). If the number with units 0 has the last one digit 0

Let the last two digits be $c_{0}$, and let the last two digits of the other two be $a5$, $b5$, then $\overline{\mathrm{a}_{5}} \times \overline{\mathrm{b}_{5}} = 100ab + 50(a + b) + 25$, if $(a + b)$ is odd, then the last two digits of the product are 75; if $(a + b)$ is even, then the last two digits of the product are 25, then multiplying by $c_{0}$, regardless of what $c$ is, the last three digits can only be 000, 250, 500, 750. In summary, the last three digits of the product have four possibilities: 000, 500, 250, 750. Therefore, the answer is: 4.