Ranking at depth 4
Model's reasoning and response:
To solve this problem, we need to compare each state against the goal state and determine how many constraints are satisfied. The goal state is:

- Block C is on the table.
- Block D is on block C.
- Block B is on block D.
- Block A is on block B.

Let's evaluate each state:

### State 18
- Block C is on the table. ✅
- Block D is not on block C. ❌
- Block B is on block C. ❌
- Block A is on the table, not on block B. ❌

**Constraints satisfied: 1**

### State 20
- Block C is on the table. ✅
- Block D is not on block C. ❌
- Block B is on block D. ✅
- Block A is on the table, not on block B. ❌

**Constraints satisfied: 2**

### State 21
- Block C is on the table. ✅
- Block D is not on block C. ❌
- Block B is on block D. ✅
- Block A is on block B. ✅

**Constraints satisfied: 3**

### State 22
- Block C is on the table. ✅
- Block D is not on block C. ❌
- Block B is on block D. ✅
- Block A is on the table, not on block B. ❌

**Constraints satisfied: 2**

### State 24
- Block C is on the table. ✅
- Block D is on block B, not on block C. ❌
- Block B is on block C. ❌
- Block A is on the table, not on block B. ❌

**Constraints satisfied: 1**

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

```ranking
21, 20, 22, 18, 24
```

State 21 satisfies the most constraints, followed by states 20 and 22, which satisfy two constraints each. States 18 and 24 satisfy only one constraint each.

Final ranking:
Rank 1: State ID 21
State Description: Block A is now on block B and is clear. Block B is on block D and is not clear. Block C is on the table and is clear. Block D is on the table and is not clear. The hand is empty.

Rank 2: State ID 20
State Description: Block A is on the table and clear. Block B is on block D and clear. Block C is on the table and clear. Block D is on the table and not clear. The hand is empty.

Rank 3: State ID 22
State Description: Block A is on the table and is clear. Block B remains on block D and is clear. Block C is clear and on the table. Block D is not clear and is on the table. The hand is empty.

Rank 4: State ID 18
State Description: Block A is on the table and clear. Block B is on block C and clear. Block C is on the table and not clear. Block D is on the table and clear. The hand is empty.

Rank 5: State ID 24
State Description: Block A is on the table and clear. Block B is on block C and not clear. Block C is on the table and not clear. Block D is on block B and clear. The hand is empty.

