|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.|