W - wolf, G - goose, M - mouth
1. Woman takes G and crosses the river.
1st bank | 2nd bank
W, M | G
2. She leaves G on the opposite second bank and turns back.
1st bank | 2nd bank
W, M | G
3. She takes W and goes with him to the bank where G already is.
1st bank | 2nd bank
M | G, W and woman
4. She takes G back to the first bank and leaves W on the second bank.
1st bank | 2nd bank
G, M | W
5. Woman leaves G on the first and takes M to the second bank.
1st bank | 2nd bank
G | W, M
6. She leaves M on the second bank and returns to the first bank.
7. Takes G and delivers it to the second bank.
1st bank | 2nd bank
| G, W, M and woman
Answer: 7 crossings.