ERRATA – SMART MOVES January 11, 2012
Proof in Discovering Geometry

Smart Moves Back Cover and Sample

SM Back cvr


Chapter 1   Warm Up Puzzles

1.1   Color Network Puzzles

1.2   Square Route Puzzles

1.3   Container Puzzles

1.4   Sequential Movement Puzzles

1.5   Cryptarithm Puzzles

1.6   Robot Programming Puzzles

Chapter 2   The Game of Racetrack

2.1   Racetrack

2.2   Mathematical Connections: Vectors

Chapter 3   Movement Puzzles

3.1   Coin Puzzles

3.2   Sliding Block Puzzles

3.3   Queen Bee Puzzles

3.4   Mini Robot Puzzles

3.5   Mathematical Connections: Archimedean Tilings

Chapter 4  Tour Puzzles

4.1   Rook’s Tour Puzzles

4.2   King’s Tour Puzzles

4.3   Knight’s Tour Puzzles

4.4   Mathematical Connections: Euler Paths

Chapter 5  Magic Square Puzzles

5.1   Introduction to Magic Squares

5.2   3x3 Magic Squares

5.3   4x4 Magic Squares

5.4   5x5 Magic Squares

5.5   6x6 and 7x7 Magic Squares

5.6   8x8 Magic Squares

5.7   12x12 Magic Squares

Chapter 6   Sequential Reasoning and Algebra

6.1   Algebraic Magic Square Puzzles

6.2   Squaring the Square Puzzles

6.3   Number Chase Puzzles

Chapter 7   Sequential Reasoning and Geometry

7.1   Angle Chase Puzzles


A.1   Racetracks

A.2   Playing Boards

A.3   Properties of Algebra

A.4   Properties of Geometry

A.5   Hints

A.6   Answers

A.7   Proofs

Sample Sequential Reasoning Puzzles


Color Network Puzzle
Each circle is to be colored Red (R), Yellow (Y), or Blue (B).  However no two vertices of a triangle are permitted to be the same color. What must be the color of the circle marked with a question mark? 


 Tour Puzzles

A knowledge of chess is not necessary in order to solve these puzzles. A rook moves horizontally or vertically, but not diagonally. Fill in the missing numbers 1- 49 for puzzle 14. For puzzle 20, fill in the missing numbers to generate a continuous path in each square.


Rook's Tour Puzzle 14 h        Rook's Tour Puzzle 20

    Image017          Image014


Mathematical Connections: Euler Paths

If all the edges of a network, called a graph in Graph Theory, can be covered without retracing any edge, then the graph has an Euler path. If all edges of a graph can be covered without repetition and you can return to the starting point, then the graph has an Euler circuit.


Magic Squares

 A Magic Square is a square array of distinct integers such that the numbers in any row, column, or main diagonals, have the same sum (called the magic sum). The magic square below is a normal 4x4 magic square.


 A magic square puzzle is an incomplete magic square.  Complete the 5x5 magic square.  You will need to calculate the magic sum first.

                        Magic Square Puzzle 36



Angle Chase Puzzles

Students rely on their recall of geometry properties (and can review them in Appendix 4), not their protractor, when solving Angle Chase puzzles. The puzzle below uses properties of parallels, vertical angles, isosceles triangle properties, and polygon sum properties. Find the measures of all the angles in the Angle Chase puzzle below.




 This article describes four different sequential reasoning puzzles (and each puzzle has many variations). These puzzles, played as part of your school mathematics curriculum, make great classroom openers, end of period thought provokers, or for students to work on at home during school breaks. The puzzles in Smart Moves are wonderful for cooperative problem solving activities in the classroom. You can project a worksheet onto a screen as the class solves the puzzle together.  I encourage parents to participate in these games and puzzles with the entire family.  Sequential reasoning puzzles can provide a setting for children and grandparents to work on problem solving and mental exercises together. Try them.  I think you’ll see the “reason” for including them in your lesson plans.


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