This blog entry and comments give me a lot of ideas about rating system, and I am doubling ideas in my blog.

I think color changes are always give a lot of fun for competitions, so recent changes (increasing number of colors) are liked by me.

I have an idea that one can interpolate colors by some main values:
on interval [a_i, a_i+1] the color value will be color_i * (a_i+1 - rating) + color_{i + 1} * (rating - a_i))

With such formulas one can get different amazing effects (for example, around top interval use non-linear interpolation to some target color).

Something as this:


the same but with initial interval:

(this main values of colors maybe not suitable, this pictures just for clarity)

Also, one can interpolate not by rating but by absolute place of competitor.
For my opinion this will be more interesting system.

A. Watermelon

Only if w can be presented as 2m + 2k watermelon can be divided to two even parts.
So w = 2(m+k), where m, k ≥ 1, that is
(w ≥ 4 и w - even) - necessary and sufficient condition for watermelon dividing.