Shape-Shifters

1. 15 squares

2. 69 triangles

3. 56 trapezoids

Dot Matrix

1. Superimpose grids 3 and 8.

2. Superimpose grids 2, 4, and 9. No two grids in the solution can share a dot in the same place. You can solve this puzzle by quick trial and error. After picking one grid, select another that does not share any dots with the first grid. Are the leftover spaces the pattern of one of the remaining grids? If so, you have found the answer.

3. Superimpose grids 1, 3, 4, 5, 8, and 9. To solve this puzzle, look for positions where dots appear in only two of the grids. For instance, only grids 5 and 9 have a dot in the upper left corner, so the solution must include both of these grids. Similar reasoning locks in grids 1, 3, and 4. Finally, the remaining dots can be filled in by grid 8.

Stick Kin 

1. Figure 2 has five cousins: 3, 4, 6, 8, and 9.

2. The sequence is 1-5-6-9-2-3-8-4-7 (or the same thing backward). Figures 1 and 7 must be at the beginning and at the end because each has just one cousin.

3. Figure 6 is the only figure that is a cousin or second cousin to all the other figures. You can solve this without having to check every figure by noticing that Figure 1 has no sticks that touch the center and Figure 4 (and Figure 8) has four sticks that touch the center. Therefore, a figure that is second cousin to both must have exactly two sticks that touch the center, and Figure 6 is the only such figure.