That is Sierpinsky (fractal) triangle, most of the entries don't matter, you should find a way to drop these spaces.
To realize this, you may examine binomial coefficients by modulo 3.
I cannot understand most of the solutions, at least from first glance, and my own solution is rather intuitive

I calculate sequentially all binomial coefficients, then multiply them accordingly by color, all this seems to work for O(n) but still not in time. How can I improve the algorithm?

from itertools import accumulate
from math import prod

def triangle(row):
    l = len(row)
    arr = list(accumulate(range(1, (l+1)//2), lambda x, y: x * (l - y) // y, initial=1))
    arr += arr[l//2-(l%2)::-1]
    return 'RGB'[((-1)**(l%2+1) * (sum(map(prod, zip(map('RGB'.index, row), arr))) % 3))]

Then we should also add the following
+S(R1 ∩ R2 ∩ R3) = 100

😃

При подсчёте пользователей нужно пропускать все числа с цифрами 4 или 9.
Если слегка переформулировать - нужно определить, какое число будет стоять на n-м месте в ряду натуральных чисел после исключения из этого ряда всех чисел, содержащих 4 и 9.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 20 21 22 23 25 26 27 28 30 31
На 4-м месте стоит 5, на 16-м стоит 20, на 24-м - 30, и т.д.

lol! But how does this work?

Great finding! (un)fortunately it's not tested... After checking, it also fails for 4832 :-(

Here is a fixed fork

if digits(n) == digits(n*n):
        return None

What about 4762? ;)

OP solved it, closing

It is not explicitly stated, but you should consider the following restrictions.
The name of the city must come first in the line. The name of the team must be one word consisting of at least two letters, the first of which is capitalized, the rest - lowercase. Any symbols other than letters of the alphabet are not allowed in the name.