The Twelve Dots

Strategies and Hints

  1. Students construct a closed curve by completing the V part of the figure. Then, by deleting two of the points on the left side, two more solutions may be obtained. (Deleting points on the right side gives solutions that are reflections of the two shown here.)

  1. Here are the solutions with the line segments inside the rectangle:

  1. There is only 1 solution to the 9-dot problem.

Solution

Here are the remaining solutions to the 12-dot problem. There are 19 different solutions in all.