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Prob­lem

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 x d₁₀ x d₁₀₀ x d₁₀₀₀ x d₁₀₀₀₀ x d₁₀₀₀₀₀ x d_1000000

Solu­tion

A pretty straight forward solution, the only trick is to turn the sequence of natural numbers 1, 2, 3, … 11, 12, 13.. into a continuous sequence of individual numbers. I did so by taking each number and turning it into a string array of its digits (e.g. 11 –> {"1"; "1"}) and concatenating these arrays using Seq.collect.