Project Euler – Problem 40

Problem description:

http://projecteuler.net/index.php?section=problems&id=40

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

My solution:

The logic behind:

Simply put: Keep increasing n, and add n to the result until the length of the result string reaches a given number.

Solution (PHP):

<?php
function d($ønsketplass)
{

while ($loop < $ønsketplass)
{
$loop = $loop+strlen($i);
$streng .= $i;
$i++;
}

return (substr($streng,($ønsketplass-1),1));
}
echo d(1)*d(10)*d(100)*d(1000)*d(10000)*d(100000)*d(1000000);
?>

Answer

210