#40 - Champernowne's constant

18 May 2016 in Project Euler on 5%

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

0.123456789101112131415161718192021...

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

If $d_n$ represents the $n^{\text{th}}$ digit of the fractional part, find the value of the following expression: \[d_1\times d_{10}\times d_{100}\times d_{1000}\times d_{10000}\times d_{100000}\times d_{1000000}\]

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Nothing overly fancy we need to do. Just loop through all the numbers, keeping track of which digit we are at.

# file: "problem040.py"
num = 1
prod = 1
d = 1
while (d < 1000001):
    for i in range(len(str(num))):
        if (d == 1 or d == 10 or
            d == 100 or d == 1000 or
            d == 10000 or d == 100000 or
            d == 1000000):
            prod = prod * int(str(num)[i:i+1])
        d = d + 1
    num = num + 1
print(prod)

The output is,

210
0.5373719607973275 seconds.

Thus, the product is 210.