At the August 31 meeting of the SWOSU Math Club we discussed the ideas behind several classic logic puzzles. The slides contain the statement of the problems; we worked out the solutions over the course of the meeting. Just to give a taste of what we can up with, we present our solution to the first river crossing puzzle.

The statement of the problem:

A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage. There is a boat that can fit himself plus either the wolf, the goat, or the cabbage. If the wolf and the goat are alone on one shore, the wolf will eat the goat. If the goat and the cabbage are alone on the shore, the goat will eat the cabbage.

How can the farmer bring the wolf, the goat, and the cabbage across the river?

 Systematically keeping track of what items are on which side, and how many trips across the river have been made, we came up with the following steps to reach our goal. For convenience, we take the river to run south, and label the banks east and west.

At the start we have:

East bank: wolf, goat, cabbage, west bank: empty

Trip 1: Take the goat to the west bank

East: wolf, cabbage, west: goat

Trip 2: Return to east bank, leaving the goat

Trip 3: Pick up the cabbage and take it across to the west side.

East: wolf, west: goat and cabbage, but since the farmer is there he can keep the goat from eating the cabbage

Trip 4: Return to the east side, taking the goat.

East: wolf, goat (farmer is present, so he can stop the wolf from eating the goat), west: cabbage

Trip 5: Bring the wolf to the west side.

Trip 6: Return to the east side, leaving the wolf and the cabbage.

Trip 7: Take the goat to the west side, at which point we have accomplished what we needed, without anything getting eaten by anything else.