| 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. | 
|