ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
---
|
|
id: 5900f4a81000cf542c50ffbb
|
|
title: 'Problem 316: Numbers in decimal expansions'
|
|
challengeType: 5
|
|
forumTopicId: 301972
|
|
dashedName: problem-316-numbers-in-decimal-expansions
|
|
---
|
|
|
|
# --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.
|
|
|
|
# --hints--
|
|
|
|
`euler316()` should return 542934735751917760.
|
|
|
|
```js
|
|
assert.strictEqual(euler316(), 542934735751917760);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler316() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler316();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|