Explanation Approach: Condition for existing sub graphs: 1. The two sub graph cannot have the same edge. 2. The sub graphs must have only four edges. This is because we are only concerned one pair of face from each cube. 3. Each vertex is incident to one edge directed in and one edge directed out. 4. The edges of each sub graphs are labelled by all the four numbers 1, 2, 3 and 4 exactly once. Calculation: From the cube 1, it is observed that the four colours are Green, yellow, blue and red. Name the vertices as G , Y , B and R . It is known that edge corresponds to a pair of opposite faces. The two opposite sides of cube 1 is coloured as green and blue. That is G is adjacent to B . The front and back are colored as yellow and red. That is Y is adjacent to R . Top and bottom are both coloured as red. That is, loop occurs at R . Hence, the vertices of first cube is { B , G } , { R , Y } and { R , R } . Similarly the vertices of second cube is { G , R } , { R , B } and { G , Y } , the vertices of third cube is { R , Y } , { B , G } and { G , Y } and the vertices of fourth cube is { R , B } , { B , G } and { Y , Y } . Draw the graph for the first cube. Draw the graph for the second cube. Draw the graph for the third cube. Draw the graph for the fourth cube. Therefore, the above four graphs have 4 vertices and 12 edges. Draw the new pseudo graphs by combining the above four graphs. Therefore, the graph of the given instant insanity is drawn. Draw any two sub graphs H 1 and H 2 by using the approach mentioned above. The above graph H 1 denotes the front to back sides of the cube.

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 12.4, Problem 34PS

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Whether the given figure

is a solution of an Instant Insanity puzzle or not.

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Chapter 12.4, Problem 33PS

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Chapter 12 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

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Whether the given figure is a solution of an Instant Insanity puzzle or not.

Solution Summary: The author explains that the given figure is not a solution of an Instant Insanity puzzle.