C2      B2  C1      C1   
  +---+---+---+---+---+---+  
  |   |   |   |   |   |   |  
  +---+---+---+---+---+---+  
D1|   |   |   |   |   |   |A1
  +---+---+---+---+---+---+  
  |   |   |   |   |   | A |  
  +---+---+---+---+---+---+  
  |   |   |   |   |   |   |B2
  +---+---+---+---+---+---+  
D2|   |   |   |   |   |   |B1
  +---+---+---+---+---+---+  
A2|   |   |   |   |   |   |B2
  +---+---+---+---+---+---+  
   D1      D1                

Each row and column originally contained one A, one B, one C, one D and two blank squares. Each letter and number pair refers to the first or second of the four letters encountered when travelling inwards. So, for example, the C2 above the first column means that C is the second letter in that column. One letter has been inserted to get you started. Can you complete the original grid?

Two solution:

       C2      B2  C1      C1   
    +---+---+---+---+---+---+  
     | B |     | A  |     | D | C | 
    +---+---+---+---+---+---+ 
D1 |    | D  | B | C  | A  |    |A1
    +---+---+---+---+---+---+ 
     | C | B  |    | D  |     | A | 
    +---+---+---+---+---+---+ 
     |    |     | C |  A |  B | D | B2
    +---+---+---+---+---+---+ 
D2 | A | C  | D |      |    | B |B1
    +---+---+---+---+---+---+ 
A2 | D | A  |     | B | C  |    |B2
    +---+---+---+---+---+---+ 
       D1        D1               

      C2      B2  C1      C1   
     +---+---+---+---+---+---+ 
     |     | B  | A  |     | D | C | 
    +---+---+---+---+---+---+ 
D1 |     | D | B | C  | A  |    | A1
    +---+---+---+---+---+---+  
     | B |     | C | D  |     | A | 
    +---+---+---+---+---+---+ 
     | C |     |     | A | B   | D | B2
    +---+---+---+---+---+---+ 
D2 | A | C  | D |     |     | B  | B1
    +---+---+---+---+---+---+ 
A2 | D | A  |    | B  | C  |     |  B2
    +---+---+---+---+---+---+ 
         D1      D1               

pardon the formatting