63 lines
1.6 KiB
Markdown
63 lines
1.6 KiB
Markdown
---
|
|
id: 5900f4891000cf542c50ff9b
|
|
challengeType: 5
|
|
title: 'Problem 284: Steady Squares'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: 3762 = 141376. Let's call a number with this property a steady square.
|
|
|
|
Steady squares can also be observed in other numbering systems. In the base 14 numbering system, the 3-digit number c37 is also a steady square: c372 = aa0c37, and the sum of its digits is c+3+7=18 in the same numbering system. The letters a, b, c and d are used for the 10, 11, 12 and 13 digits respectively, in a manner similar to the hexadecimal numbering system.
|
|
|
|
For 1 ≤ n ≤ 9, the sum of the digits of all the n-digit steady squares in the base 14 numbering system is 2d8 (582 decimal). Steady squares with leading 0's are not allowed.
|
|
|
|
Find the sum of the digits of all the n-digit steady squares in the base 14 numbering system for
|
|
1 ≤ n ≤ 10000 (decimal) and give your answer in the base 14 system using lower case letters where necessary.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler284()</code> should return 5a411d7b.
|
|
testString: assert.strictEqual(euler284(), '5a411d7b', '<code>euler284()</code> should return 5a411d7b.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler284() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler284();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|