Match Stick Problems and Puzzles:

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Match Stick Problems and Puzzles

• Connecting Geometry, Algebra, and Problem Solving
• By Patty George
• Cerritos College

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Introduction

• Match Stick Problems and Functions
• Match Stick Puzzles and Creative Problem Solving

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Match Stick Problems and Functions

• A function is a relationship between two sets, a
  domain and a range, such that for each element in
  the domain there corresponds exactly one element
  in the range.

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Match Stick Triangles

• Here is a triangle made of 3 match sticks.
• A track of two triangles looks like this.
• A track of three triangles looks like this.

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Problem 1

• How many match sticks would it take to make a
  track of 500 triangles?

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Consider Problem Solving Strategies

• Simplify the problem.
• Make a chart.
• Look for a pattern.
• Make a generalization.
• Create a function.

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Simplify the Problem

• How many match sticks does it take to make 1
  triangle?
• How many match sticks does it take to make 2
  triangles?
• How many match sticks does it take to make 3
  triangles?
• How many match sticks does it take to make 4
  triangles?

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Make a Chart
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Look for a PatternDeconstruct the Information
in the Chart
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Make a Generalization
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Create a Function

• The function provides a general formula that can
  be used to get specific information.
• f(n)32(n-1) or f(n)2n1 where n represents the
  number of triangles and f(n) represents the
  number of match sticks.

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Solution to Problem 1

• You would need f(500)32(499)1001 match sticks
  to create a track of 500 triangles.

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A Square Match Stick Unit

• Suppose a square match stick unit is defined to
  be a square with one match stick per side.

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A Track of Square Match Stick Units

• A track of two square match stick units would
  look like this.
• A track of three square match stick units would
  look like this.

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Problem 2

• How many match sticks would you need to create a
  track of 500 square match stick units?

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What Problem Solving Strategies Can You Try?

• Simplify the problem.
• Make a chart.
• Look for a pattern.
• Make a generalization.
• Describe a function.

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Simplify the Problem

• How many match sticks does it take to make 1
  square?
• How many match sticks does it take to make 2
  squares?
• How many match sticks does it take to make 3
  squares?
• How many match sticks does it take to make 4
  squares?

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Make a Chart
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Look for a Pattern Deconstruct the Information
in the Chart
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Make a Generalization
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Create a Function

• f(n)43(n-1) or f(n)3n1 where n represents the
  number of squares and f(n) represents the number
  of match sticks.

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Solution to Problem 2

• It would take 1501 match sticks to create a track
  of 500 squares.

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Problem 3

• How many match sticks would you need to make a
  track of 500 rectangles in which each rectangle
  is two match sticks long and one match stick
  wide?
• Is there more than one answer?

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Problem 4

• How many match sticks would it take to make a 20
  by 20 match stick square that is made from
  joining square match stick units?
• Here is a 2 by 2 match stick square.

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Match Stick Puzzles

• These are match stick problems that require some
  creative problem solving.

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Problem 5

• Move only 2 matches to create 4 identical match
  stick squares.

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Problem 6

• Move two matches to form seven identical squares.

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Problem 7

• Notice this figure contains seven squares. Move
  four matches to form three squares.

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Conclusion

• Match stick problems connect ideas from geometry,
  algebra, functions and problem solving.
• Match stick puzzles require creative extension of
  problem solving.

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For More Information

• Frohlich, Gary, Connecting Mathematics
  Curriculum and Evaluation Standards for School
  Mathematics, Addenda Series Grades 9-12, National
  Council of Teachers of Mathematics, Reston, VA,
  1995.
• Holt, Michael, Math Puzzles and Games, Barnes and
  Noble Books, 1996.
• Van Delft, Pieter and Jack Botermans, Creative
  Puzzzles of the World, Key Curriculum Press,
  Berkeley, California, 1995.
• http//www.mathsonline.co.uk/nonmembers/resource/a
  lgebra/matchalg.html
• http//www.sciencenews.org/sn_arch/8_10_96/mathlan
  d.htm