The object of this puzzle is to divide the large square into four equal regions, each with the same size, shape, and number of circles. Although this puzzle may seem easy at first glance, it will soon become apparent that more than a simple trial-and-error approach is needed.

A better method is to approach the puzzle mathematically by thinking about the size and shape of each region. Since the larger square is comprised of 16 smaller squares, each of the four equal regions would be comprised of four small squares. The four squares in each region can be put together in a limited number of ways. Furthermore, since there are twelve circles that must be divided equally among the four regions, each region would have three circles. After students have analyzed the puzzle in this way, they have a better chance of solving it.

The square below can be divided into four equal regions, each with the same size, shape, and number of circles. Identify the four regions by coloring each one differently.

**Solution**

Click the arrow below to view the solution.

There is actually a second correct answer to this puzzle.

Since a picture can’t be drawn lets just call the vertical (top to bottom) A,B,C,D and the horizontal (left to right) 1,2,3,4.

A1;B1;C1;B2

A2;A3;A4;B3

B4;C4;D4;C3

D1;D2;D3;C2

With your solution, the four regions do not have equal numbers of circles