A peasant finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, the boat has room for only the peasant himself and one other item (either the wolf, the goat, or the cabbage). In his absence, the wolf would eat the goat, and the goat would eat the cabbage.
a) Solve this problem for the peasant or prove it has no solution. (Note: The peasant is a vegetarian but does not like cabbage and hence can eat neither the goat nor the cabbage to help him solve the problem. And it goes without saying that the wolf is a protected species.)

The solution is presented in explanation

Explanation:

This problem can be solved in following steps:

1) In the first round the peasant will take the goat to the other side.

2) Now, the peasant will come back alone.

3) The peasant will now take the wolf with him to other side.

4) The peasant will return with the goat to riverbank.

5) Now, he will take cabbage to the other side of the river, where the wolf is already present.

6) Peasant will leave cabbage and wolf on other side and come back to riverbank alone. Since, wolf does not eat cabbage.

7) Now, finally the peasant will take goat to the other side of river.

In this way, all three of them shall be transported to the other side of the river without eating each other.

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