47fc3c6761
* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.5 KiB
Markdown
51 lines
1.5 KiB
Markdown
---
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id: 5900f4891000cf542c50ff9b
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title: 'Problem 284: Steady Squares'
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challengeType: 5
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forumTopicId: 301935
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dashedName: problem-284-steady-squares
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---
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# --description--
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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: ${376}^2 = 141376$. Let's call a number with this property a steady square.
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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: $c37^2 = aa0c37$, 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.
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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.
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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 as a string in the base 14 system using lower case letters where necessary.
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# --hints--
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`steadySquares()` should return a string.
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```js
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assert(typeof steadySquares() === 'string');
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```
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`steadySquares()` should return the string `5a411d7b`.
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```js
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assert.strictEqual(steadySquares(), '5a411d7b');
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```
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# --seed--
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## --seed-contents--
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```js
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function steadySquares() {
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return true;
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}
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steadySquares();
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```
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# --solutions--
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```js
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// solution required
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```
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