79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
70 lines
1.6 KiB
Markdown
70 lines
1.6 KiB
Markdown
---
|
|
id: 5900f4a81000cf542c50ffbb
|
|
challengeType: 5
|
|
title: 'Problem 316: Numbers in decimal expansions'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Let p = p1 p2 p3 ... be an infinite sequence of random digits, selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
|
|
It can be seen that p corresponds to the real number 0.p1 p2 p3 ....
|
|
It can also be seen that choosing a random real number from the interval [0,1) is equivalent to choosing an infinite sequence of random digits selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
|
|
|
|
For any positive integer n with d decimal digits, let k be the smallest index such that pk, pk+1, ...pk+d-1 are the decimal digits of n, in the same order.
|
|
Also, let g(n) be the expected value of k; it can be proven that g(n) is always finite and, interestingly, always an integer number.
|
|
|
|
For example, if n = 535, then
|
|
for p = 31415926535897...., we get k = 9
|
|
for p = 355287143650049560000490848764084685354..., we get k = 36
|
|
etc and we find that g(535) = 1008.
|
|
|
|
Given that , find
|
|
|
|
Note: represents the floor function.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler316()</code> should return 542934735751917760.
|
|
testString: assert.strictEqual(euler316(), 542934735751917760, '<code>euler316()</code> should return 542934735751917760.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler316() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler316();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|