Ranking at depth 9
Model's reasoning and response:
To rank the states, we need to evaluate how many goal constraints each state satisfies. The goal constraints are:

1. Row 1:
   - tile_1-1: white
   - tile_1-2: black
   - tile_1-3: white

2. Row 2:
   - tile_2-1: black
   - tile_2-2: white
   - tile_2-3: black

Let's evaluate each state:

### State 100
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: occupied (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### State 101
- tile_1-1: occupied (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: black (correct)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 3 (tile_2-1, tile_2-2, tile_2-3)**

### State 103
- tile_1-1: clear (not white)
- tile_1-2: occupied (not black)
- tile_1-3: clear (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### State 106
- tile_1-1: occupied (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### State 108
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: occupied (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### State 110
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: black (correct)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 3 (tile_2-1, tile_2-2, tile_2-3)**

### State 111
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: occupied (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### State 112
- tile_1-1: clear (not white)
- tile_1-2: occupied (not black)
- tile_1-3: clear (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied: 2 (tile_2-2, tile_2-3)**

### Ranking
Based on the number of constraints satisfied, the ranking from best to worst is:

```ranking
101, 110, 100, 103, 106, 108, 111, 112
```

Final ranking:
Rank 1: State ID 101
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is occupied by robot1. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color black. Colors white and black are available for switching.

Rank 2: State ID 110
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color black. Colors white and black are available for switching.

Rank 3: State ID 100
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is occupied by robot1. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_2-1, holding color black. Colors white and black are available for switching.

Rank 4: State ID 103
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is occupied by robot1. Tile tile_1-3 is clear. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 5: State ID 106
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is occupied by robot1. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color white. Colors white and black are available for switching.

Rank 6: State ID 108
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is occupied by robot1. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-3, holding color white. Colors white and black are available for switching.

Rank 7: State ID 111
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is occupied by robot1 holding color black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_2-1, holding color black. Colors white and black are available for switching.

Rank 8: State ID 112
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is occupied by robot1 holding color black. Tile tile_1-3 is clear. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

