Generate 4 grids in 4 directions and move each of them step by step to fullfil a middle grid like tetris

Basically I have 4 grids Left, Right, Top, Bottom. Player can choose each of them and move all the blocks on that grid to the Middle grid to fulfill it, like tetris from 4 directions:

      |0 0 0|
      |0 0 0|             (0 is empty, 1 is generated block)
      |0 0 1| 
       _ _ _         Bottom->Mid  Right->Mid  Top->Mid   Left->Mid     
|0 0 0|0 0 0|0 1 0|    |1 0 0|     |1 1 0|     |1 1 1|    |1 1 1|  
|0 0 0|0 0 0|0 1 1|    |1 0 0|     |1 1 1|     |1 1 1|    |1 1 1| -> Win! Generate 
|1 0 0|0 0 0|0 1 1|    |0 0 0|     |0 1 1|     |0 1 1|    |1 1 1|    another game.
       _ _ _
      |0 0 0|
      |1 0 0|
      |1 0 0|

The point here is to make sure there is at least 1 way player can combine all 4 grids.

What I've tried so far is generate the right order first (Left->Right->Top....), then generate all the blocks 1 by 1. When a block is generated, i perfomn a check with the generated order (move all the blocks in Left to Mid, then Right then Top...) to see if its still working, the code is similar to this:

// (left->right, top->right->botttom->left, top... it doesn't have to be all 4 directions)
Random the right direction order. 

Generate all possible coordinates from all the directions from the path above.
Initialize an empty list to store all chosen coordinates.

While(!(Generate enough x*x block))
{
    Remove one coordinate from all possible coordinates and add it into chosen list.

    if (!(Perform a check with the right order and the chosen list.))
        Remove it from the chosen list.

}

The problem here is a block can be wrong at this point, but it can become right when another block is generated, so i can't choose to add or remove it and go to the next one:

          |0 0 0|                                      |0 0 1|
          |0 0 1|                                      |0 0 1|
          |0 0 1|                                      |0 0 1|
           _ _ _                                        _ _ _
    |0 1 0|0 0 0|0 0 0|                          |0 1 0|0 0 0|0 0 0|
    |1 0 0|0 0 0|0 0 0|                          |1 0 0|0 0 0|0 0 0|
    |1 0 0|0 0 0|0 0 0|                          |1 0 0|0 0 0|0 0 0|
           _ _ _                                        _ _ _
          |0 1 0|                                      |0 1 0|
          |0 1 0|                                      |0 1 0|
          |0 0 0|                                      |0 0 0|
 At this point the logic is wrong          But if I add 1 more block to the
  with Top->Left->Bottom order.               top grid, it'll become right. 

So is there a way I can generate each block and check its logic? Or is there a better way, algorithm to do it?