2018-09-30 22:01:58 +00:00
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---
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id: 5900f4f11000cf542c510002
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title: 'Problem 388: Distinct Lines'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 302052
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2021-01-13 02:31:00 +00:00
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dashedName: problem-388-distinct-lines
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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Consider all lattice points (a,b,c) with 0 ≤ a,b,c ≤ N.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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From the origin O(0,0,0) all lines are drawn to the other lattice points. Let D(N) be the number of distinct such lines.
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2018-09-30 22:01:58 +00:00
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You are given that D(1 000 000) = 831909254469114121.
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Find D(1010). Give as your answer the first nine digits followed by the last nine digits.
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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`euler388()` should return 831907372805130000.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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assert.strictEqual(euler388(), 831907372805130000);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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function euler388() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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euler388();
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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