Which of the following states satisfy the capacity constraints of the 12-9-7 water jug puzzle? (3, 2, 7) (3, 4, 5) (1, 9, 2) (0, 4, 8)

The 12-9-7 water jug puzzle involves three jugs with capacities of 12, 9, and 7 units respectively. The goal is to measure out certain quantities of water, given these constraints.

Let's check each of the given states:

1. (3, 2, 7): This state does not satisfy the capacity constraints because the second jug, which has a capacity of 9 units, is said to contain only 2 units. This is possible. However, the third jug, which has a capacity of 7 units, is said to contain 7 units. This is also possible. So, this state is possible.

2. (3, 4, 5): This state does not satisfy the capacity constraints because the second jug, which has a capacity of 9 units, is said to contain 4 units. This is possible. However, the third jug, which has a capacity of 7 units, is said to contain 5 units. This is also possible. So, this state is possible.

3. (1, 9, 2): This state does not satisfy the capacity constraints because the first jug, which has a capacity of 12 units, is said to contain 1 unit. This is possible. However, the second jug, which has a capacity of 9 units, is said to contain 9 units. This is also possible. But, the third jug, which has a capacity of 7 units, is said to contain 2 units. This is also possible. So, this state is possible.

4. (0, 4, 8): This state does not satisfy the capacity constraints because the third jug, which has a capacity of 7 units, is said to contain 8 units. This is not possible as it exceeds the capacity of the jug. So, this state is not possible.

So, the states that satisfy the capacity constraints of the 12-9-7 water jug puzzle are (3, 2, 7), (3, 4, 5), and (1, 9, 2).