Explanation
To find the minimum number of moves, we need to track the state of both containers: the 9 L container and the 4 L container. We aim to reach a state where one container holds exactly 6 L.
Initial State: (0,0)
| Move # |
Action |
9 L Container |
4 L Container |
| 1 |
Fill the 9 L container |
9 L |
0 L |
| 2 |
Pour from 9 L to 4 L |
5 L |
4 L |
| 3 |
Empty the 4 L container |
5 L |
0 L |
| 4 |
Pour from 9 L to 4 L |
1 L |
4 L |
| 5 |
Empty the 4 L container |
1 L |
0 L |
| 6 |
Pour from 9 L to 4 L |
0 L |
1 L |
| 7 |
Fill the 9 L container |
9 L |
1 L |
| 8 |
Pour from 9 L to 4 L (filling it) |
6 L |
4 L |
Explanation of the final move:
The 4 L container already had 1 L. To fill it, we need exactly 3 L more. We pour that 3 L from the 9 L container.
Remaining in 9 L container: 9−3=6 L.
The task is completed in exactly 8 moves.
Final Answer:
The smallest number of moves needed is 8.
The correct option is (a).
