## Lake crossing

Purpose

This problem solving activity has a logic and reasoning focus.

Student Activity

Tui needs to row her pet ferret, pet rabbit and a bale of hay across to the island where she lives.
The problem is that she can handle only one thing at a time.

If she leaves the ferret with the rabbit, the ferret will kill the rabbit.

If she leaves the rabbit with the hay, the rabbit will eat the hay.
This will cause a problem on either side of the water.

Can she successfully get the ferret, rabbit and hay across to her island without losing anything?

Specific Learning Outcomes
• Follow a chain of reasoning.
• Recognise logical arguments.
Description of Mathematics

This is a logic problem. Logic is an important part of mathematics and of the curriculum.

If students choose to act this out or use equipment, a careful record of each step should be made. By using a table or drawing a diagram, the method will be more evident. As in any problem solving situation, a written record should be encouraged in order for students to be able to justify their solution, or to identify an error made in the process.

Other related Logic and Reasoning problems include Space Crossing, Level 5.

Required Resource Materials
Activity

### The Problem

Tui needs to row her pet ferret, pet rabbit and a bale of hay across to the island where she lives. The problem is that she can handle only one thing at a time.
If she leaves the ferret with the rabbit, the ferret will kill the rabbit.
If she leaves the rabbit with the hay, the rabbit will eat the hay. This will cause a problem on either side of the water.

Can she successfully get the ferret, rabbit and hay across to her island without losing anything?

### Teaching Sequence

1. Pose the problem and ask for the students' thoughts on how to approach it.
2. Have the students make suggestions for the first couple of "moves". Ask:
How could we keep track of the moves taken? (Diagrams, symbols and words)
3. As students work on the problem, ask if they have found the quickest way to get everyone across.
4. Remind the students that they need record the steps taken in order to justify their solution.
5. Share solutions and discuss the various recorded methods. Ask:
Are you convinced that you have found the fewest number of trips? How do you know?

#### Extension

The next time that Tui goes off her island, she needs to bring back her dog, another ferret, another rabbit and some hay. The dog would the kill the ferret if Tui is not around and we know all of the other difficulties.

This time Tui can take two things across the water with her. Can she get them all across successfully?

Can you make up some more problems like this? Can you solve them?

### Solution

In the  solution below, T = Tui, F = ferret, R = rabbit and H = hay.

 On the land On the water On the island T, F, R, H F, H T, R (to island) T ( to land) R H T, F (to island) T, R (to land) F R T, H (to island) T ( to land) F, H T, R (to island) T, F, R, H

Can you do this in fewer than 7 crossings?

#### Solution to the Extension

 On the land On the water On the island T, D, F, R, H D, R T, F, H (to island) T (to land) F, H T, D, R (to island) T, D, F, R, H

That was a lot easier than the original problem. Can it be done if Tui can only take one thing across with her?

The answer to that is no. If she takes the dog or the hay, there will be trouble with the ferret and the rabbit. If she takes the ferret the rabbit will eat the hay. If she takes the rabbit the ferret and the dog will be left together.

Attachments