The Cupcake Problem

For the solution, click "Read More," below.

The Horse Puzzle

For the solution, click "read more," below.

Origami Square Folding Problem

This problem has surprisingly many solutions.  For the solution, click here.

Dots and Polygons Game

For printable game boards, click here.

The Shaded Triangles Problem

For the solution, click here.

Toothpick Perimeter Problem

It is possible to make an area as small as 2 square units (and perhaps smaller?) with 12 toothpicks!  For the solution, click here.

Stacked Dice

Solution: The sum of any two opposite faces of a die is 7.  So, excluding the top face, the sum of the numbers on the 3-dice tower is always equal to 7 x 2 x 3 = 42, and it doesn't matter how we arrange the dice.  The only thing that affects the total sum is the number showing on the top, which can be any number from 1 to 6.  So the minimum sum is 42 + 1 = 43 and the maximum sum is 42 + 6 = 48.  For 20 dice, the minimum sum is 7 x 2 x 20 + 1 = 281 and the the maximum sum is 7 x 2 x 20 + 6 = 286.  For n dice, the minimum sum is 7 x 2 x n + 1 and the maximum sum is 7 x 2 x n + 6.