Husbands and wives

Question

There are 5 married couples wanting to cross a river by a boat. The boat can carry at most 3 persons at a time and of course cannot cross the river by itself with no one on board.

The problem is that all the husbands are extremely jealous. So no woman can be in the presence of another man unless her husband is also present. Even a woman alone in a boat at a bank which has other men on that shore without her husband is not permissible.

In other words at no point of time can women outnumber men on bank or shore because that would mean some woman is husband-less!

It is assumed that everyone knows how to row and all persons on the boat disembark and board at the same time.

Given the constraints provided, what is the minimum number of one-way trips needed to transport these 10 people at the opposite bank? Please indicate also the arrangements.

I found 11 one-way trips. Can anyone help?

Answer 1

I've found this

1. $W_1 \to H_1$
2. $W_1,W_2 \to H_1,H_2$
3. $W_1,W_2,W_3 \to H_1,H_3$
4. $W_1,H_1,W_2,H_2 \to W_3,H_3$
5. $W_2,H_2,H_3,H_4,H_5 \to H_1,W_1$
6. $W_2,H_2,W_3,H_3,W_4,H_4 \to H_5,W_5$
7. $W_1,H_1,W_2,H_2,W_3,H_3,W_4,H_4 \to H_5$
8. $W_1,H_1,W_2,H_2,W_3,H_3,W_4,H_4,W_5,H_5$