If something doesn't seem tractable, try flipping between algebraic and geometric interpretations of a problem. Problems 1 and 3 fell to this approach.
Specific solutions (or suggestive handwaving):
Problem 1:
I thought of it like parity - going left to right, each unichromatic edge doesn't change the color, while each bichromatic edge does. So to have an overall change, we need either 1 bichromatic edge, or 3 (1 and 2 that cancel), or 5 (1 and 4 that cancel)...
Problem 2:
I couldn't understand this one at first. After checking Wikipedia, I think that Rn refers to the space that each point in the sequence lies within. An example of a finite sequence... (read more)
Strategies that I've found helpful:
If something doesn't seem tractable, try flipping between algebraic and geometric interpretations of a problem. Problems 1 and 3 fell to this approach.
Specific solutions (or suggestive handwaving):
Problem 1:
I thought of it like parity - going left to right, each unichromatic edge doesn't change the color, while each bichromatic edge does. So to have an overall change, we need either 1 bichromatic edge, or 3 (1 and 2 that cancel), or 5 (1 and 4 that cancel)...
Problem 2:
I couldn't understand this one at first. After checking Wikipedia, I think that Rn refers to the space that each point in the sequence lies within. An example of a finite sequence... (read more)