45 lines
1.4 KiB
Markdown
45 lines
1.4 KiB
Markdown
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---
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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: 3762 = 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: 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.
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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 in the base 14 system using lower case letters where necessary.
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# --hints--
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`euler284()` should return 5a411d7b.
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```js
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assert.strictEqual(euler284(), '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 euler284() {
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return true;
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}
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euler284();
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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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