Solution for problem #1
We have two sides of the river, side A and side B. The people start at side A and their goal is to get to side B. There are two adults, A1 and A2, and two children, K1 and K2.
1. K1 and K2 go to side B.
2. K1 goes back to side A but K2 stays at side B.
3. A1 goes to side B.
4. K2 goes to side A so only A1 is at side B.
5. K1 and K2 go to side B.
6. K1 goes back to side A.
7. A2 goes to side B.
8. K2 goes back to side A.
9. Finally, K1 and K2 go to side B together.
Solution for problem #2
We have two sides of the river, side A and side B. The people start at side A and their goal is to get to side B. There are three adults, A1, A2 and A3, and two children, K1 and K2.
1. K1 and K2 go to side B.
2. K1 goes back to side A but K2 stays at side B.
3. A1 goes to side B.
4. K2 goes back to side A.
5. K1 and K2 go to side B.
6. K1 goes back to side A but K2 stays at side B.
7. A2 goes to side B.
8. K2 goes back to side A.
9. K1 and K2 go to side B.
10. K1 goes back to side A but K2 stays at side B.
11. A3 goes to side B.
12. K2 goes back to side A.
13. Finally, K1 and K2 go to side B together.
Solution for problem #3
There are two sides of the river, side A and side B. We have one-hundred adults, A1, A2 and so on, and two children, K1 and K2.
1. K1 and K2 go to side B.
2. K2 goes back to side A
3. A1 goes to side B. There is now one adult and one kid at side B.
4. K1 goes back to side A.
5. Repeat 99 times.
6. Finally, the kids go over in the same boat.
There is a pattern that both children go over, one child comes back, an adult goes over, one child comes back. No matter how many adults there are, this pattern will always work.