Klauz Oppenheim is putting together an animation as an art project for school. He wants to portray his message using familiar objects that his audience will be able to relate to, so he bought 16 sour skittles (individually wrapped) and placed them in a square. He will take 17 images, beginning with all of the skittles and taking away one per frame until none are left.
Klauz does not want to confuse his audience by flashing a sequence of strange ugly shapes, so he would like to maximize the beauty of his animation. For any frame we can assign a number, the amount of symmetries that the frame has (the order of its symmetry group), and so to an animation we can assign a number, the sum of the values of its frames.
Each skittle has a color and so the way they are initially laid out is important. You can tell Klauz which skittle to remove and when, but unfortunately you cannot tell him how to place them on the surface. He already went and glued them to the surface, and if he buys any more skittles he'll be over his budget. This is how he arranged them.
- There are 17 frames. There is the one pictured above, and then one skittle disappears per frame until none are left. Your answer is the sequence of skittles that you will remove.
- Symmetry is measured per frame and then the sum is taken. For each frame the symmetry value is the order of its symmetry group, including the identity. That is, every line of symmetry gives 1 point, and every rotation gives 1 point.
- Your goal is to achieve the best possible symmetry score (and thus the most aesthetically pleasing animation).
- Color matters when counting symmetries.
- Color especially matters to us because as a reward for our help, Krauz has offered to let us eat the final skittle. Every color is a different flavor and our favorite flavor is grape (purple)! The frame with 1 skittle yields 12 points for purple, 10 points for green, 8 points for red, and 2 points for blue.
- The frame with no skittles yields 0 points.
EDIT: GentlePurpleRain points out that 1 skittle would have infinite score. For that matter, so would 0. To deal with these cases I have added a new rule and clarified 0.