This puzzle comes from a rich historical tradition that dates back to the 19th century when matches were first manufactured. Invented in 1827 by the British chemist John Walker, matches soon replaced the tinder boxes and flints that people had formerly used to light fires. As matches grew in popularity and became ubiquitous later in the century, they spawned a new form of entertainment—matchstick puzzles—which became quite popular when several match companies printed these puzzles on their boxes. Capitalizing on this interest, publishers began to print books of matchstick puzzles. Near the end of the 19th century, many people had developed a personal repertoire of these puzzles that they used to challenge friends and acquaintances. The toothpick puzzle presented here is modeled after the classical matchstick puzzles. For safety reasons, these puzzles use ﬂat toothpicks instead of matches. (Round tooth-picks are not recommended, as they tend to roll.)
This puzzle has six challenges, each of which starts with 36 toothpicks arranged to form 13 small squares. Students then either move or remove a given number of toothpicks to form the numbers of geometric shapes stated. Once students have a solution, they should use the dot paper to record it. The dot paper can also be used to solve the challenges if toothpicks aren’t available—students can simply draw the figure and then erase lines instead of removing or moving toothpicks. Several of the challenges have multiple correct answers. Students can be encouraged to find all of the possible answers for each challenge.
The challenges presented here require patience and persistence to solve. However, they tend to be a bit easier for students who have well-developed spatial-relationship skills. Often, these students are not the top students, and their ability to solve these puzzles faster than their peers is a great esteem builder. Conversely, this type of puzzle often frustrates those students who usually do well at traditional school tasks and provides them with a real challenge. This role reversal is often beneficial for both sets of students.
In addition to using their spatial skills, students can also utilize logical thinking when working on these puzzles. While each challenge may eventually be solved by trial-and-error, taking a few minutes to think logically about the problem will often reveal the solution. Another key puzzle-solving trait that students will need to develop when working on these puzzles is persistence—students can’t solve a puzzle if they give up. You will need to encourage students to be persistent and to keep trying until they solve the puzzles.
As the teacher, you are encouraged to try the puzzles yourself before giving them to your students. You may find them difficult, as do many adults who are linear thinkers, but don’t assume that your students will experience this same level of difficulty. You may be surprised at how well some of them do with these puzzles. Good luck!
Arrange 36 flat toothpicks to form 13 small squares as shown below. Use the toothpicks to solve the challenges.
- Remove 4 toothpicks to leave 8 small squares.
- Move 6 toothpicks to make 14 small squares.
- Remove 8 toothpicks to leave 9 small squares.
- Remove 4 toothpicks to leave 5 small squares and 4 rectangles.
- Move 4 toothpicks to make 1 rectangle and 10 small squares.
- Remove 8 toothpicks to leave 5 small squares and 1 large square.