The Problem
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
The Solution
Well, this seems simple enough. We just have to write a function to find d
.
It's all map
and reduce
after that...right?
let d n =
let rec generate i total =
let s = i.ToString()
if n >= total && n <= total + s.Length then
s.[n - total - 1]
else
generate (i + 1) (total + s.Length)
int(generate 1 0) - int('0')
The function d
contains an internal recursive function called generate
.
generate
takes as input a digit position, i
and an accumulator total
which
stores the length of the string of digits. It converts i
into a string of
digits. If the n
we're looking for is between total
and total + s.Length
then
we know we have found the part of the sequence that contains the magic digit
we're looking for. If so, it returns that digit. Otherwise, it recurses, adding
1 to i
and adding the number of digits of i
to the total.
Now to solve the problem:
[0..6]
|> Seq.map (fun n -> d (pown 10 n))
|> Seq.reduce (fun acc item -> acc * item)
We start with the sequence 0..6
and use Seq.map
and pown
to generate the
sequence 1, 10, 100, etc.
Next, we simply use Seq.reduce
to multiply each number in the resulting sequence
into a single value. That is our answer.