83 lines
1.5 KiB
Markdown
83 lines
1.5 KiB
Markdown
---
|
||
id: 5900f4531000cf542c50ff65
|
||
challengeType: 5
|
||
title: 'Problem 230: Fibonacci Words'
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
For any two strings of digits, A and B, we define FA,B to be the sequence (A,B,AB,BAB,ABBAB,...) in which each term is the concatenation of the previous two.
|
||
|
||
Further, we define DA,B(n) to be the nth digit in the first term of FA,B that contains at least n digits.
|
||
|
||
Example:
|
||
|
||
Let A=1415926535, B=8979323846. We wish to find DA,B(35), say.
|
||
|
||
The first few terms of FA,B are:
|
||
1415926535
|
||
8979323846
|
||
14159265358979323846
|
||
897932384614159265358979323846
|
||
14159265358979323846897932384614159265358979323846
|
||
|
||
Then DA,B(35) is the 35th digit in the fifth term, which is 9.
|
||
|
||
Now we use for A the first 100 digits of π behind the decimal point:
|
||
14159265358979323846264338327950288419716939937510
|
||
58209749445923078164062862089986280348253421170679
|
||
|
||
and for B the next hundred digits:
|
||
|
||
82148086513282306647093844609550582231725359408128
|
||
48111745028410270193852110555964462294895493038196 .
|
||
|
||
Find ∑n = 0,1,...,17 10n× DA,B((127+19n)×7n) .
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>euler230()</code> should return 850481152593119200.
|
||
testString: assert.strictEqual(euler230(), 850481152593119200);
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function euler230() {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
euler230();
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
```js
|
||
// solution required
|
||
```
|
||
|
||
</section>
|