by Dave and Michelle Youngs
The Puzzle Corner this month is a toothpick puzzle which comes from The Moscow Puzzles: 359 Mathematical Recreations by Boris Kordemsky (1971). The puzzle is an array of 24 toothpicks arranged to form a three by three square grid. Students are presented with a variety of challenges that require them to create a different number of geometric shapes by moving and/or removing various numbers of toothpicks. Our version has added two more challenges than were present in the original, bringing the total up to ten.
Unlike many toothpick puzzles, this one is very open-ended in the sense that almost every challenge has more than one solution. This increases students' chances of success and makes it a good puzzle to build confidence in the area of spatial relationships. It also provides the opportunity to introduce or review some basic geometric terms such as "congruent", "irregular," and "hexagon."
Each puzzle requires 24 flat toothpicks. Flat toothpicks are recommended rather than rounded ones because the flat ones do no roll around on the table, making them easier to manipulate. Students also need a copy of the student page for a list of the challenges. You may wish to provide students with scratch paper on which to sketch their solutions if the back of the paper does provide enough room.
As with all Puzzle Corner activities, you are encouraged to do the puzzle yourself before you give it to your students. Give yourself and your students ample time to discover the solutions. Be sure students know that they do not need to solve the challenges in order. If they are stuck on one, they should move on to the next to avoid too much frustration. As an extension, have those students who solve the puzzles quickly develop a challenge of their own and give it to their classmates to solve.