When k ranks at the nth place, there are n-2 numbers besides n and k, and the number of staggered rows is Dn-2.

When k is not ranked in the n th place, then the n th place will be reconsidered as the new "k position". At this time, every dislocation of the remaining n- 1 numbers, including k, is equivalent to the dislocation when there are only n- 1 numbers (only k bits will be replaced by n bits). The staggered number is Dn- 1.

For less frequent arrangements, enumeration can be used.

When n= 1, there is only one completely arranged and not staggered, and D 1=0. When n=2, there are two complete permutations, namely 1, 2 and 2, 1, the latter is staggered, and D2= 1.

When n=3, there are six complete permutations, namely 1, 2, 3; 1、3、2; 2、 1、3; 2、3、 1; 3、 1、2; 3,2, 1, of which only 3,2 and 2,3, 1 are staggered, and D3=2. Similarly, we can know that D4=9.

Total dislocation permutation is called "a wonderful problem of combinatorial number theory" by the famous mathematician Euler (1707- 1783), and it is two special cases of "error envelope problem". A person wrote n different letters, corresponding to n different envelopes, and he put them all in the wrong envelopes. How many ways can you put them in the wrong envelope?