7. If (1) $a, b, c, d$ all belong to $\{1,2,3,4\}$; (2) $a \neq b, b \neq c, c \neq d, d \neq a$; (3) $a$ is the smallest value among $a, b, c, d$, then the number of different four-digit numbers $\overline{a b c d}$ that can be formed is $\qquad$ .
7. When $\overline{a b c d}$ contains exactly 2 different digits, it can form $C_{4}^{2}=6$ different four-digit numbers. When $\overline{a b c d}$ contains 3 different digits, it can form $C_{3}^{1} C_{2}^{1} C_{2}^{1}+C_{2}^{1} C_{2}^{1}=16$ different four-digit numbers. When $\overline{a b c d}$ contains exactly 4 different digits, it can form $P_{3}^{3}=6$ different four-digit numbers. Therefore, the total number of four-digit numbers that meet the requirements is $6+16+6=28$.