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Champernowne's constant

Problem 40

Published on Friday, 28th March 2003, 06:00 pm; Solved by 48543; Difficulty rating: 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 dn represents the nth digit of the fractional part, find the value of the following expression.

d1 × d10 × d100 × d1000 × d10000 × d100000 × d1000000