The challenge is to stack four cubes such that each side of the stack shows four different images.

These are the nets of 4 cubes. Build a tower so that on each vertical wall no color is repeated, that is all 4 colors appear. Arrange the four cubes in a stack, on top of each other so that the front, back, left and right faces each contain a red, blue, green and white square in any order.

1. Do NOT look at the next page, try to solve this puzzle with your own method for at least 10 minutes. Post your result here (pictures of all sides of your stack). Explain your strategy. Does it work or not?
2. Using a graph to represent the symbols on opposite sides of each cube. Prepare a graph with four vertices. Assign one symbol to each vertex. For each cube, add three color-coded edges to the graph. Each of these three arcs will connect the vertices corresponding to the symbols on each pair of opposite faces.You need to find and draw two distinct sub-graphs, each of which contains one arc of each color and in which each of the four vertices has degree two (i.e. is a two-node). (Draw your sub-graphs here).
3. Label one sub-graph Left-Right and the other Front-Back. Label the clockwise direction by each graph. The arcs of each color, read clockwise, indicate how each cube is to be arranged in the tower.

The challenge is to stack four cubes such that each side of the stack shows four different images. These are the nets of 4 cubes. Build a tower so that on each vertical wall no color is repeated, that is all 4 colors appear. Arrange the four cubes in a stack, on top of each other so that the front, back, left and right faces each contain a red, blue, green and white square in any order. The stack might look like this from the front. Symbols can be used for the cube faces instead of colors. Symbols can be used for the cube faces instead of colors. a) Do NOT look at the next page, try to solve this puzzle with your own method for at least 10 minutes. Post your result here (pictures of all sides of your stack). Explain your strategy. Does it work or not? b) Using a graph to represent the symbols on opposite sides of each cube. Prepare a graph with four vertices. Assign one symbol to each vertex. For each cube, add three color-coded edges to the graph. Each of these three arcs will connect the vertices corresponding to the symbols on each pair of opposite faces. You need to find and draw two distinct sub-graphs, each of which contains one arc of each color and in which each of the four vertices has degree two i.e. is a 'two-node'). (Draw your sub-graphs here). c) Label one sub-graph "Left-Right" and the other "Front-Back". Label the clockwise direction by each graph. The arcs of each color, read clockwise, indicate how each cube is to be arranged in the tower. The challenge is to stack four cubes such that each side of the stack shows four different images. These are the nets of 4 cubes. Build a tower so that on each vertical wall no color is repeated, that is all 4 colors appear. Arrange the four cubes in a stack, on top of each other so that the front, back, left and right faces each contain a red, blue, green and white square in any order. The stack might look like this from the front. Symbols can be used for the cube faces instead of colors. Symbols can be used for the cube faces instead of colors. a) Do NOT look at the next page, try to solve this puzzle with your own method for at least 10 minutes. Post your result here (pictures of all sides of your stack). Explain your strategy. Does it work or not? b) Using a graph to represent the symbols on opposite sides of each cube. Prepare a graph with four vertices. Assign one symbol to each vertex. For each cube, add three color-coded edges to the graph. Each of these three arcs will connect the vertices corresponding to the symbols on each pair of opposite faces. You need to find and draw two distinct sub-graphs, each of which contains one arc of each color and in which each of the four vertices has degree two i.e. is a 'two-node'). (Draw your sub-graphs here). c) Label one sub-graph "Left-Right" and the other "Front-Back". Label the clockwise direction by each graph. The arcs of each color, read clockwise, indicate how each cube is to be arranged in the tower