Partitioning a Square

Supplies: Inch dot paper in six by six inch squares, pencil, colored pencils or markers, scissors. Poster board or butcher paper and Scotch tape or glue for displaying students' solutions.

In a six by six inch square, connect the two points marked by small circles, going through all dots inside the square. Only horizontal and vertical moves are allowed. Color your picture with two different colors.

Figure 1. Click on figure for printable version

When you get a solution, place it on the class poster. Only new solutions can be placed there. No duplicates! (No mirror images or rotations!) How many different solutions are there?

What is the perimeter of each part of a partition?
What is the area of each part?

One way to check if two solutions A and B are different: Cut one solution, say A, into its two parts. See if one of the parts of A is congruent to (same size and shape as) either of the parts of B. (You may need to rotate or flip the part!)

Thus far we have found twelve different solutions. They are given below. Are there any more? If you find any, please send them to baggett@nmsu.edu.

Figure 2 Click on image for larger version.

Examples of students' work:

Figure 3