# Pentomino Challenge

These are pentominoes, with their letter codes:

F: | I: | L: | M: |

N: | P: | T: | U: |

V: | X: | Y: | Z: |

This challenge is more difficult than it looks.

Create four yes/no questions which uniquely classify each pentomino.

Examples of such questions are:

- Does it have rotational symmetry?
- Does it have reflection symmetry?
- Is it the net of an open box?
- Does it have point symmetry?

The idea is to create a set of questions where **no pentomino has the same answers as another**.

## Example

Rotational Symmetry | Reflection Symmetry | Open Box | Point Symmetry | |

F | no | no | yes | no |

I | yes | yes | no | yes |

L | no | no | no | no |

M | no | yes | yes | no |

N | yes | no | yes | yes |

P | no | no | no | no |

T | no | yes | yes | no |

U | ||||

V | ||||

X | ||||

Y | ||||

Z |

... so these four questions do not work ... **the answers for T are the same as for M ... ! **

Can YOU think of four questions which will work?

(You can discuss this at the forum.)

This is based upon an investigation by L Mottershead. *Sources of Mathematical Discovery*