Cubix Shadow

Introduction

The Cubix Shadow is aDALESTapplication. It shows the shadows of an invisible structure and the number of cubes in the structure. The user should reconstruct the structure with the exact number of cubes and the exact shadows. Some problems have more than one solutions. There are three sets of problems – easy, moderate and hard. They are described in a text file, so everyone can add new problems. New structures can be defined manually or by using theCubix Editorapplication

The restriction to use predefined number of cubes is essential, because this makes the solution much more difficult and requires a better understanding of how shadows are casted

Activities

- Create a structure with predefined shadow
- Create a structure with predefined shadow and number of cubes
- Determine the minimal and maximal number of cube which produce the same shadow
- Solve the 3x3x3 shadow puzzle using any 27 cubes, then solve it with 21 cubes, 15 cubes, and finally with 9 cubes
- Determine the maximal and minimal number of cube needed to reproduce the shadow of NxNxN cube
- By using theCubix Editorcreate new structures and let other users try them
- Find cases when the shadows of a structure can be used to calculate the area of the structure
- Find counter examples
- Try to find a set of shadows for which the ratio of maximal/minimal number of cubes is biggest or smallest
- Using a fixed number of cubes try to produce the biggest (or smallest) shadows
- Study the features of shadows of symmetrical (rotated) structures