1. 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 number among $a, b, c, d$.

Then, the number of different four-digit numbers $\overline{a b c d}$ that can be formed is $\qquad$.
(提示: $\overline{a b c d}$ consists of 2 different digits, then it must be that $a=$ $c, b=d$. Therefore, there are $\mathrm{C}_{4}^{2}=6$ such numbers. $\overline{a b c d}$ consists of 3 different digits, then $a$ is uniquely determined, when $c=a$, $b, d$ have 2 ways to be chosen; when $c \neq$ $a$, $c$ has 2 ways to be chosen, and $b=d$ is the remaining number, so there are $\mathrm{C}_{4}^{3} \times(2$ $+2)=16$ such numbers. $\overline{a b c d}$ consists of 4 different digits, $a=1$, so there are $3!=6$ such numbers. In total, there are $6+16+6=28$ different four-digit numbers.)