This activity has a logic and reasoning focus.

In the Federated Universe, the Galpons and the Exetrarts do not get on.

The Exetrarts will dematerialise any Galpon they are in close contact with, provided they are in the majority.

The Galpons are peaceful and won't harm any Exetrarts they find themselves with.

Three Galpons and three Exetrarts are on a crippled space transport to the planet Jeeboh.

Therefore they need to transfer to a space shuttle in which only two creatures can travel at a time.

All of the Galpons can drive the shuttle but only one Exetrart can drive.

Can they all get to the surface of Jeeboh safely?

This is a logic problem, and 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.

Related problems include: Lake Crossing I.

Objects to represent Galpons and three Exetrarts.

### The Problem

In the Federated Universe, the Galpons and the Exetrarts do not get on.

The Exetrarts will dematerialise any Galpon they are in close contact with, provided they are in the majority.

The Galpons are peaceful and won't harm any Exetrarts they find themselves with.

Three Galpons and three Exetrarts are on a crippled space transport to the planet Jeeboh.

Therefore they need to transfer to a space shuttle in which only two creatures can travel at a time.

All of the Galpons can drive the shuttle but only one Exetrart can drive.

Can they all get to the surface of Jeeboh safely?

### Teaching sequence

- Pose the problem and ask for the students initial thoughts and suggestions for the first couple of "moves". Ask:
*How could we keep track of the moves taken?*(diagrams, symbols and words) - As the students are working on the problem and start to find solutions, ask:
*Is this the quickest way to get everyone across?*

Can you get everyone across in fewer moves? - Remind the students that they need to justify their answer. This means that they will need to record the steps taken.
- Share solutions. One group may like to demonstrate with objects while the rest of the class counts the trips taken. Ask:
*Did anyone else use the same number of trips? Did you use the same method?*

Did anyone get a different number of trips?

Are you convinced that you have found the fewest number of trips? How do you know? - Have students to see if they can follow the reasoning used by other pairs.

#### Extension

Can you generalise this problem? Can you solve them?

#### Solution

In the solution below, g1, g2, g3 are the Galpons and e1, E2, E3 are the Exetrarts and e1 has done the space shuttle driver’s course.

On the space transport | In the shuttle | On Jeeboh |

(g1, g2, g3, e1, E2, E3 temporarily) | ||

g1, g3, e1, E3 | g2, E2 (to Jeeboh) | (g2, E2 temporarily) |

(g1, g2, g3, e1, E3 temporarily) | g2 ( to transport) | E2 |

g1, g2, g3 | e1, E3(to Jeeboh) | (e1, E2, E3 temporarily) |

(g1, g2, g3, e1 temporarily) | e1 (to transport) | E2, E3 |

g1, e1 | g2, g3 (to Jeeboh) | (g2, g3, E2, E3 temporarily) |

(g1, g2, e1, E2 temporarily) | g2, E2 (to transport) | g3, E3 |

g2, E2 | g1, e1 (to Jeeboh) | (g1, g3, e1, E3 temporarily) |

(g1, g2, E2, E3 temporarily) | g1, E3 (to transport) | g3, e1 |

E2, E3 | g1, g2 (to Jeeboh) | (g1, g2, g3, e1 temporarily) |

(e1, E2, E3 temporarily) | e1 (to transport) | g1, g2, g3 |

E3 | e1, E2 (to Jeeboh) | (g1, g2, g3, e1, E2 temporarily) |

(e1, E3 temporarily) | e1 (to transport) | g1, g2, g3, E2 |

e1, E3 (to Jeeboh) | ||

g1, g2, g3, e1, E2, E3 |

Can you do this in fewer than 13 trips?