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Problem 40: Champernowne''s constant

curriculum/challenges/english/blocks/project-euler-problems-1-to-100/5900f3941000cf542c50fea7.md

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--description--

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

0.123456789101112131415161718192021...

It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.

If d<sub>n</sub> represents the n<sup>th</sup> digit of the fractional part, find the value of the following expression.

d<sub>1</sub> × d<sub>10</sub> × d<sub>100</sub> × d<sub>1000</sub> × d<sub>10000</sub> × d<sub>100000</sub> × d<sub>1000000</sub>

--hints--

champernownesConstant(100) should return a number.

js
assert(typeof champernownesConstant(100) === 'number');

champernownesConstant(100) should return 5.

js
assert.strictEqual(champernownesConstant(100), 5);

champernownesConstant(1000) should return 15.

js
assert.strictEqual(champernownesConstant(1000), 15);

champernownesConstant(1000000) should return 210.

js
assert.strictEqual(champernownesConstant(1000000), 210);

--seed--

--seed-contents--

js
function champernownesConstant(n) {

  return true;
}

champernownesConstant(100);

--solutions--

js
function champernownesConstant(n) {
  let fractionalPart = '';
  for (let i = 0; fractionalPart.length <= n; i++) {
    fractionalPart += i.toString();
  }

  let product = 1;
  for (let i = 0; i < n.toString().length; i++) {
    const index = 10 ** i;
    product *= parseInt(fractionalPart[index], 10);
  }

  return product;
}