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Four Cubes Problem

Graph Theory Master's Presentation
by

Leah Owens

on 22 July 2013

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Transcript of Four Cubes Problem

"Tantilizing" or "Instant Insanity"
The Four Cube Problem
Instant Insanity Game
Is This Possible?
The 4 Multi-Colored Cubes
Multi-Graphs
How Do We Solve It?
Composite Graph
2-Regular Spanning Submultigraph
Directions:

Open the package. Notice that there are four different colors on each side of this stack of blocks. You may never, EVER see them this way again. Now, mix them up and then restack them so that there are again four colors, all different, showing on each side.
1) How many ways can the first cube be set on the table to begin?



2) How many different ways can the second cube be placed on top of the first one?


3) How many ways can you stack all four cubes on top of one another?
Cube #1



Cube #2



Cube #3



Cube #4
For each cube, we can construct a multi-graph (allowing loops) of order 4 and size 3.

Vertex Set: {R,G,B,Y)

Opposite Faces are Adjacent
Cube #1 Cube #2






Cube #3 Cube #4
M'
B
B
B
B
B
B
G
G
G
G
G
G
R
Y
Y
Y
Y
Y
Y
R
R
R
R
R
R
B
G
Y
R
R
R
B
B
B
G
G
G
Y
Y
Y
R
B
G
Y
1
1
1
2
2
2
3
3
3
4
4
4
M''
R
B
G
Y
R
B
G
Y
1
1
2
2
3
3
4
4
Full transcript