Champernowne's constant

An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021...

It can be seen that the 12^th digit of the fractional part is 1.

If d_n represents the n^th digit of the fractional part, find the value of the following expression.

d₁ × d₁₀ × d₁₀₀ × d₁₀₀₀ × d₁₀₀₀₀ × d₁₀₀₀₀₀ × d_1000000

---

Idea

Naive solution.

Directly get the ith digit by calculation.

---

from functools import reduce
from operator import mul
from math import ceil

def get_digit(ith):
    start = 0
    for digit_number, total in enumerate(map(lambda i: pow(10, i) * 9, range(6)), 1):
        if ith > total * digit_number:
            start += total
            ith -= total * digit_number
        else:
            break
    k, r = ceil(ith / digit_number), (ith-1) % digit_number
    return int(str(start + k)[r])

get_digit(11)

0

get_digit(12)

1

get_digit(1)

1

def solve():
    return reduce(mul, map(get_digit, map(lambda i: pow(10, i), range(7))), 1)

solve()

210