27A. Distinct Candies

Move two candies from the first container to the fourth, then one candy from the second container to the third. The final counts are 0, 1, 3, and 4.

It is impossible to make the five counts distinct with only five candies.

There is only one container, so no moves are needed.

Move one candy from the first container to the third. The final counts are 0, 1, and 2.

Transfer three candies from the first container to the sixth, two from the second to the fifth, and one from the third to the fourth. The final counts are 0, 1, 2, 4, 5, and 6.

Both containers are empty, so no move is possible and their counts remain equal.

Move one candy to the other container. The final counts are 0 and 2.

The final counts can be 0, 1, 2, 3, and 4. Transfer two candies from the first container to the fifth and one from the second to the fourth. At least three moves are needed.

Transfer two candies from the first container to the fourth and one from the second to the third. The final counts are 8, 9, 11, and 12. Three moves are necessary.

Transfer three candies from the first container to the seventh, two from the second to the sixth, and one from the third to the fifth. The final counts are 0, 1, 2, 3, 4, 5, and 6. At least six moves are necessary.