36・17 One day, the boss gives letters to the secretary to type at different times, each time placing the letter on top of the secretary's pile. The secretary, when available, takes the letter from the top of the pile to type. Suppose there are 5 letters, and the boss gives them in the order $1,2,3,4,5$. Among the following sequences, which one cannot be the order in which the secretary types the letters?
(A) 12345.
(B) 24351.
(C) 32415.
(D) 45231.
(E) 54321.
(38th American High School Mathematics Examination, 1987)
［Solution］(A) is possible: after typing 1, type 2; after typing 2, type 3; $\cdots$, after typing 4, type 5, and finally type 5;
(B) is possible: when typing 2 (1 is at the bottom), 3 and 4 come; after finishing 4, when typing 3, 5 comes, then continue to type 5 and 1;
(C) is possible: start typing in the order of 3, 2, 1; when typing 2, 4 comes; after finishing 4 and 1, 5 comes;
(E) is possible: after all five letters arrive, type them in sequence;
(D) is impossible: after typing 4 and 5, the next should be 3.
Therefore, the answer is $(D)$.