This week’s activity consists of five related puzzles that should challenge students. Matchstick (I have substituted toothpicks) puzzles have been a staple feature of recreational mathematics for years. The puzzles presented here were adapted from some that appeared in The Moscow Puzzles by Boris Kordemsky (available from Dover Publications, Inc.)
This type of puzzle often requires patience and persistence to solve. These puzzles are easier for students who have well-developed spatial-relationship skills. Often, these students are not the “top” students. In fact, this type of puzzle is often very frustrating for those students who do well at traditional school tasks. Because of this, these puzzles are useful, challenging those who have an easy time with most school work and giving success to others who need it.
It is important to try these puzzles yourself. If you find them difficult, don’t despair; they are difficult for many adults, especially those who are linear thinkers. Don’t assume, however, that all of your students will have as hard a time with the puzzles as you did. You may be surprised (at how well some of them do at these puzzles).
A positive aspect of these puzzles, for both students and adults alike, is that they exercise spatial-relationship skills as well as logic skills. After solving one of the five puzzles, you learn to “see” things, both visually and logically, that help solve the remaining puzzles.
Have fun and good luck!
Puzzle 1: Make two squares of different sizes by removing two toothpicks.
Puzzle 2: Make three congruent squares by moving three toothpicks.
Puzzle 3: Make three congruent squares by moving four toothpicks.
Puzzle 4: Make seven squares, not all congruent, by moving two toothpicks. You may cross one toothpick over another.
Puzzle 5: Make 10 squares, not all congruent, by moving four toothpicks. You may cross one toothpick over another.
Solutions
Click the arrow below to view the solutions.
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The dashed lines in the diagrams indicate the toothpicks that were moved, the dotted lines indicate toothpicks that were removed.
Puzzle 1: Make two squares of different sizes by removing two toothpicks.
Puzzle 2: Make three congruent squares by moving three toothpicks.
Puzzle 3: Make three congruent squares by moving four toothpicks.
Puzzle 4: Make seven squares, not all congruent, by moving two toothpicks. You may cross one toothpick over another.
Puzzle 5: Make 10 squares, not all congruent, by moving four toothpicks. You may cross one toothpick over another.
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If you’re interested in more fun puzzles check out the Puzzle Play book for Grades 4-8.