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Count the Number

Source: 2000 National High School Mathematics League, Exam One, Problem 12

March 11, 2020

Problem Statement

If (1)a,b,c,d∈{1,2,3,4};(2)a≠b,b≠c,c≠d,d≠a;(3)a=min⁡{a,b,c,d}(1)a,b,c,d\in\{1,2,3,4\};(2)a\neq b,b\neq c,c\neq d,d\neq a;(3)a=\min\{a,b,c,d\}, then the number of different 4-digit-number abcd‾\overline{abcd} is________.
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