Test a simple river-crossing puzzle

Here's how the farmer can get across the river with the sheep in the fewest trips:

1. Farmer crosses the river alone.
2. Farmer returns alone.
3. Farmer takes the sheep across the river.

That's it! It takes just three trips.

To get the farmer and the sheep across the river with the smallest number of trips, the farmer needs to follow these steps:

1. The farmer takes the sheep across the river. (Trip 1)
2. He leaves the sheep on the other side and returns back alone. (Trip 2)
3. The farmer crosses again with the sheep. (Trip 3)

In this scenario, the farmer and the sheep make it across the river with a total of 3 trips.

To get the farmer and the sheep to the other side of the river using the boat in the smallest number of trips, the farmer can follow these steps:

1. First, the farmer takes the sheep across the river and leaves it on the other side.
2. The farmer then returns to the starting side of the river, using the boat.
3. The farmer then takes himself across the river, leaving the boat on the other side.
4. The farmer then takes the boat back to the starting side of the river, picks up the sheep, and takes it to the other side.

This process requires a total of 3 trips to get the farmer and the sheep to the other side of the river.

The reason this is the smallest number of trips is that the farmer cannot leave the sheep alone on the starting side of the river, as the sheep might wander off or be in danger. By taking the sheep across first, then returning for himself, and then going back for the sheep, the farmer ensures that the sheep is always supervised and safely transported across the river.

To get the farmer and the sheep across the river using the smallest number of trips, the farmer can follow these steps:

1. The farmer takes the sheep across the river first in the boat and leaves it on the other side.
2. The farmer goes back alone to the original side of the river in the boat.
3. The farmer takes the sheep back with him to the original side of the river is not necessary, we change our approach here. Now the farmer leaves the original side in the boat alone again but this time he counts as 'another person'. The second trip was fetching the farmer back to join what was equivalent to the first animal (item) across the river.

Modified step 3. Now there are two of each (equivalent of the same 2).

4. In the last trip the Two people ('original person and what is an item - animal or another animal equivalent that IS an empty person' square the circle) and one empty seat, the original farmer's 4th trip causes the item/other animal equivalent to be discarded.

The farmer can get himself and the sheep to the other side of the river in 3 trips. Here's how:

1. First, the farmer takes the sheep across the river in the boat and leaves it on the other side.
2. The farmer then returns alone in the boat to the original side.
3. Next, the farmer leaves the boat on the original side and walks a short distance away with the sheep to prevent it from jumping back into the boat while he's away.
4. The farmer goes back to the boat and rows it to the other side of the river alone.
5. Finally, the farmer walks back to get the sheep and brings it across the river in the boat.

By following these steps, the farmer makes 3 trips across the river (1st trip with the sheep, 2nd trip alone, and 3rd trip with the sheep). This is the smallest number of trips needed to ensure the safety of the sheep, as leaving the sheep unattended on either side with the boat would result in the sheep using the boat to cross the river on its own.