Intermixed sequence of Push and pop operations why is this sequence not possible

Ok, So the program always pushes 0-9 in that order, so looking at each line, we work out which order the pushes and pops happen

**The first line.**   - Stack is
Pushes 0, 1, 2, 3, 4  - [0, 1, 2, 3, 4]
Pops   4, 3, 2, 1, 0  - []
Pushes 5, 6, 7, 8, 9  - [5, 6, 7, 8, 9]
Pops   9, 8, 7, 6, 5  - []

**Second line**  - Stack is  
Pushes 0, 1, 2   - [0, 1, 2]  
Pops   2, 1      - [0]  
Pushes 3, 4      - [0, 3, 4]  
Pops   4, 3      - [0]  
Pushes 5, 6      - [0, 5, 6]  
Pops   6, 5      - [0]  
Pushes 7, 8      - [0, 7, 8]  
Pops   8, 7      - [0]  
Pushes 9         - [0, 9]  
Pops   9, 0      - []  

**Third line**    - Stack is   
Pushes 0          - [0]  
Pops   0          - []  
Pushes 1, 2, 3, 4 - [1, 2, 3, 4]  
Pops   4,         - [1, 2, 3]  
Pushes 5, 6       - [1, 2, 3, 5, 6]  
Pops   6, 5, 3    - [1, 2]  
Pushes 7, 8       - [1, 2, 7, 8]  
Pops   8          - [1, 2, 7]   
Pops   ?            

The next pop MUST be 7, because it was pushed before 8, it cannot be 1.

This is not difficult to solve. You just start writing the sequence until you find the first popped number; then cross it out and continue. Now we can see why the third sequence cannot occur:

0 // Pop 0
-
1 2 3 4 // Pop 4
1 2 3
1 2 3 5 6 // Pop 6
1 2 3 5 // Pop 5
1 2 3 // Pop 3
1 2
1 2 7 8 // Pop 8
1 2 7 // And here it fails; you cannot possibly pop a 1 from the stack