**"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