---
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
```
