You could begin by asking the students who they think would make the first move, and why. If necessary, guide them through the solution (given in full below) and the reasoning behind each move. More able students will be able to do this unassisted.

Students could be asked to describe the thought processes involved in reaching the solution. The most important piece of information is that the boat has a maximum weight limit of 80 kg, which means that the man and the woman must travel on their own and the dog can only travel with one of the boys (not the man or woman). The boys can travel either together or alone.

Discuss the most sensible starting move with the group, and then allow the students sufficient time to work out further moves. With small groups, you could even recreate the problem using a model train set, which would particularly help visual–spatial learners.

Seven crossings are needed:

1. The farmer first takes the turkey across the river.
2. He returns, with the boat empty.
3. He carries the wheat across to the other bank.
4. He takes the turkey back with him.
5. He brings over the fox.
6. He recrosses the river, with the boat empty.
7. He returns with the turkey again.

This table shows which items are on each bank after each step. The farmer is always with the boat:

Key: T = Turkey, F = Fox, W = Wheat, R = River, * = Boat.

Eleven crossings are needed:

1. The two boys row across the river.
2. One of the boys brings the boat back, while the other stays on the far bank.
3. The woman rows herself over.
4. The boy on the far side brings the boat back.
5. The two boys go over again.
6. One remains on the far bank and the other comes back with the boat again.
7. The man goes across.
8. The boy on the far side brings the boat back.
9. One of the boys takes the dog over.
10. He leaves the dog with his parents and comes back for the last time.
11. The two boys cross the river.

Key: M = Man, W = Woman, B = Boy, D = Dog, R = River, * = Boat.

(The man and woman are interchangeable.)

‘Left’ and ‘right’ in the solution below are from the observer’s point of view, not the engine driver’s.

1. The engine goes to the left along the main line, and then backs up the siding and pushes truck C under the bridge.
2. The engine returns to the main line, backs to the right, and enters the right hand end of the siding.
3. The driver couples the two trucks together and returns with them to a central position on the main line, where he uncouples truck C.
4. The engine backs to the right, taking truck D with it, and pushes the truck up the right hand end of the siding and under the bridge.
5. The engine returns to the main line, where it is coupled to truck C.
6. Again the engine backs to the right, enters the siding, and leaves truck C beside signal-post B.
7. Now the engine returns to the main line, proceeds to the left, and backs up the left-hand end of the siding.
8. The driver couples the engine to truck D, and pulls the truck to signal-post A, where he leaves it.
9. Finally, the engine is taken back to its original position on the main line.

• In groups, ask students to design a poster to illustrate the steps and processes involved in the solution.
• Students could devise their own problem and challenge others to solve it.

As with The puzzled farmer, students could design a poster or other method outlining the solution.

• What happens if the bridge moves position?
• Can this be solved if the engine is in a different starting position?