49 lines
1.1 KiB
Markdown
49 lines
1.1 KiB
Markdown
---
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id: 5900f4761000cf542c50ff88
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title: 'Problem 265: Binary Circles'
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challengeType: 5
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forumTopicId: 301914
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dashedName: problem-265-binary-circles
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---
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# --description--
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2N binary digits can be placed in a circle so that all the N-digit clockwise subsequences are distinct.
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For N=3, two such circular arrangements are possible, ignoring rotations:
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For the first arrangement, the 3-digit subsequences, in clockwise order, are: 000, 001, 010, 101, 011, 111, 110 and 100.
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Each circular arrangement can be encoded as a number by concatenating the binary digits starting with the subsequence of all zeros as the most significant bits and proceeding clockwise. The two arrangements for N=3 are thus represented as 23 and 29: 00010111 2 = 23 00011101 2 = 29
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Calling S(N) the sum of the unique numeric representations, we can see that S(3) = 23 + 29 = 52.
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Find S(5).
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# --hints--
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`euler265()` should return 209110240768.
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```js
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assert.strictEqual(euler265(), 209110240768);
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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 euler265() {
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return true;
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}
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euler265();
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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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