Java sudoku solver not changing empty cells

I am in the process of writing a sudoku solver (still need to write the box check and actually complete the program) but I'm testing it as I know. The puzzle I'm testing right now is "very easy" as in there is only one empty cell in any row/column. THe puzzle starts with "empty" cells as zeros. My issues is that when I run the program and print out the puzzle after solve() is called, the zeros aren't changing and the original puzzle is just printed out. Not sure what my issue is, would appreciate some direction!

public ArrayList<Integer> create(){
 
     ArrayList<Integer> possible = new ArrayList<Integer>(); 
 
     for(int i=1; i<10; i++){
         possible.add(i);
     }
     return possible;
 }
 public sudoku( int size )
 {
     SIZE = size;
     N = size*size;
 
     Grid = new int[N][N];
     for( int i = 0; i < N; i++ ) 
         for( int j = 0; j < N; j++ ) 
             Grid[i][j] = 0;
 }
 
 public void solve()
 { 
     int a, b, c, d, i, j, k, l; 
 
     int count = 0;
     int value= 0;
 
     for(i=0; i<N;i++){
         for(j=0; j<N;j++){  
             if(Grid[i][j]==0){
 
                 ArrayList<Integer> possible = create();
 
                 //check row             
                 for(a=0; a<N;a++){
                     for(b=0; b<N; b++){  
                         if(Grid[a][0]==possible.get(a)){
                             possible.set(a, 0);
                         }
                     }
                 }
                 //check column
                 for(c=0; c<N;c++){
                     for(d=0; d<N;d++){  
                         if(Grid[0][d]==possible.get(d)){
                             possible.set(d,0);
                         }
                     }
                 }
                 for(k=0; k<9; k++){
                     if(possible.get(k)!=0){
                         count++;
                     }
                 }
                 if(count==1){
                     for(l=0; l<9; l++){
                         if(possible.get(l)!=0){
                             value=possible.get(l);
                         }
                     }
                 }
                 Grid[i][j]=value;
             }
         }
     }
 }
 

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