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1. | Cut a unit square into 5 triangles, all of which have area less than .21. |
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2. |
Cut a square into 5 triangles whose areas are in geometric progression. | 
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3. |
Cut a square into 5 isoceles triangles, no two of which are similar. (solution by Evan Whitney) |
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4. |
Cut a square into 7 isoceles right triangles, no two of which are congruent. (second solution by Bob Wainwright) |
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5. |
Cut a square into 8 right triangles, all having one leg twice as long as the other, no two of which are congruent. |
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6. |
Cut a square into 8 acute triangles. (solution by David Epstein) |
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7. |
Cut a unit square into 8 triangles with sides no larger than 5/8. | 
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8. |
Pack 7 equilateral triangles with side 1/2 into a unit square. | 
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