45 lines
1.4 KiB
Markdown
45 lines
1.4 KiB
Markdown
---
|
|
id: 5900f4891000cf542c50ff9b
|
|
title: 'Problem 284: Steady Squares'
|
|
challengeType: 5
|
|
forumTopicId: 301935
|
|
dashedName: problem-284-steady-squares
|
|
---
|
|
|
|
# --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.
|
|
|
|
# --hints--
|
|
|
|
`euler284()` should return 5a411d7b.
|
|
|
|
```js
|
|
assert.strictEqual(euler284(), '5a411d7b');
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function euler284() {
|
|
|
|
return true;
|
|
}
|
|
|
|
euler284();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|