freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-230-fibonacci-words.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4531000cf542c50ff65	Problem 230: Fibonacci Words	5	301874	problem-230-fibonacci-words

--description--

For any two strings of digits, A and B, we define F_{A,B} to be the sequence (A, B, AB, BAB, ABBAB, \ldots) in which each term is the concatenation of the previous two.

Further, we define D_{A,B}(n) to be the n^{\text{th}} digit in the first term of F_{A,B} that contains at least n digits.

Example:

Let A = 1\\,415\\,926\\,535, B = 8\\,979\\,323\\,846. We wish to find D_{A,B}(35), say.

The first few terms of F_{A,B} are:

$$\begin{align} & 1\,415\,926\,535 \\ & 8\,979\,323\,846 \\ & 14\,159\,265\,358\,979\,323\,846 \\ & 897\,932\,384\,614\,159\,265\,358\,979\,323\,846 \\ & 14\,159\,265\,358\,979\,323\,846\,897\,932\,384\,614\,15\color{red}{9}\,265\,358\,979\,323\,846 \end{align}$$

Then D_{A,B}(35) is the {35}^{\text{th}} digit in the fifth term, which is 9.

Now we use for A the first 100 digits of π behind the decimal point:

$$\begin{align} & 14\,159\,265\,358\,979\,323\,846\,264\,338\,327\,950\,288\,419\,716\,939\,937\,510 \\ & 58\,209\,749\,445\,923\,078\,164\,062\,862\,089\,986\,280\,348\,253\,421\,170\,679 \end{align}$$

and for B the next hundred digits:

$$\begin{align} & 82\,148\,086\,513\,282\,306\,647\,093\,844\,609\,550\,582\,231\,725\,359\,408\,128 \\ & 48\,111\,745\,028\,410\,270\,193\,852\,110\,555\,964\,462\,294\,895\,493\,038\,196 \end{align}$$

Find \sum_{n = 0, 1, \ldots, 17} {10}^n × D_{A,B}((127 + 19n) × 7^n).

--hints--

fibonacciWords() should return 850481152593119200.

assert.strictEqual(fibonacciWords(), 850481152593119200);

--seed--

--seed-contents--

function fibonacciWords() {

  return true;
}

fibonacciWords();

--solutions--

// solution required