1. | Cut a unit square into 5 triangles, all of which have area less than .21. |

2. | Cut a square into 5 triangles whose areas are in geometric progression. |

3. | Cut a square into 5 isoceles triangles, no two of which are similar. (solution by Evan Whitney) |

4. | Cut a square into 7 isoceles right triangles, no two of which are congruent. (second solution by Bob Wainwright) |

5. | Cut a square into 8 doms (right triangles having one leg twice as long as the other), no two of which are congruent. |

6. | Cut an L-shaped region made of 3 squares into 8 doms, no two of which are congruent. (solution by George Sicherman) |

7. | Cut a square into 8 acute triangles. (solution by David Epstein) |

8. | Cut a unit square into 8 triangles with sides no larger than 5/8. |

9. | Pack 7 equilateral triangles with side 1/2 into a unit square. |