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Reducing Squares

Reducing Squares

Reducing Squares belongs to a category of puzzles called “matchstick puzzles” which were very popular in America during the last century. Most adults in those days carried small boxes of matches with them to light the many candles or lamps in their homes. Many of these same people had a favorite repertoire of matchstick puzzles to share with friends. Matchstick puzzles were just one of the indicators of a strong general interest in puzzles of all kinds during the 1800s newspapers in those days included a much greater variety of puzzles than today’s ubiquitous crossword puzzles and word jumbles.

In Reducing Squares toothpicks are substituted for matchsticks for safety reasons. I have found that flat toothpicks work the best because they do not roll. Each student will need 24 toothpicks for this particular puzzle. You may wish to have students make small paper envelopes in which to keep their toothpicks when they are not working on the puzzle.

Arrange 24 toothpicks as shown below. Each challenge asks to you reduce the number of squares in the arrangement by taking away different numbers of toothpicks. See if you can solve each challenge, and then come up with a challenge of your own. Make a record of your solutions.


Challenge #1: Reduce the number of squares to two by removing eight toothpicks.

Challenge #2: Reduce the number of squares to five by removing four toothpicks.

Challenge #3: Reduce the number of squares to five by removing eight toothpicks.

Challenge #4: Reduce the number of squares to nine by removing four toothpicks.

Challenge #5: Create you own challenge and make a record of it.


Click the arrow below to view the solutions.

Reducing Squares asked students to remove various numbers of toothpicks from an arrangement to leave different numbers of squares. The solutions appear below. Please note that in some situations, the solution shown is only one of several possibilities.

Reducing Squares Solutions

One Response to Reducing Squares

  1. One of the things I like about these puzzles are there may be multiple answers. All too often students find an answer and then stop working! In real life most problems have multiple answers and that idea in itself is IMPORTANT!
    The other thing that is good about this is the cost factor for the teacher. Today teachers more and more have to buy their own materials. My granddaughter’s teacher requested prior to Christmas and again at the end of the year that, IF any family wanted to give a gift to her, she would sincerely appreicate a gift card to a store where she could buy materials for her classroom. I’d not seen that before and it is a GREAT idea.
    Dale F. Wolfgram

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