Problem :

Suppose that n cards numbered 1,2,3,.....,n are arranged in a row. The task is to pick them up in numerically increasing order, working repeatedly from left to right.

For example ;

If numbers are [7,11,8,6,4,5,9,12,1,13,10,2,3].
In the first move pick : [1,2,3].
In the second move pick : [4,5].
In the third move pick : [6].
In the fourth move pick : [7,8,9,10].
In the fifth move pick : [11,12,13].

How many of the n! possible orderings of the cards will the n cards be picked up in exactly two moves ?