47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
---
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id: 5900f50c1000cf542c51001e
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title: 'Problem 415: Titanic sets'
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challengeType: 5
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forumTopicId: 302084
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dashedName: problem-415-titanic-sets
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---
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# --description--
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A set of lattice points S is called a titanic set if there exists a line passing through exactly two points in S.
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An example of a titanic set is S = {(0, 0), (0, 1), (0, 2), (1, 1), (2, 0), (1, 0)}, where the line passing through (0, 1) and (2, 0) does not pass through any other point in S.
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On the other hand, the set {(0, 0), (1, 1), (2, 2), (4, 4)} is not a titanic set since the line passing through any two points in the set also passes through the other two.
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For any positive integer N, let T(N) be the number of titanic sets S whose every point (x, y) satisfies 0 ≤ x, y ≤ N. It can be verified that T(1) = 11, T(2) = 494, T(4) = 33554178, T(111) mod 108 = 13500401 and T(105) mod 108 = 63259062.
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Find T(1011) mod 108.
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# --hints--
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`euler415()` should return 55859742.
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```js
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assert.strictEqual(euler415(), 55859742);
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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 euler415() {
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return true;
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}
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euler415();
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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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