1.4 KiB
1.4 KiB
id | challengeType | title |
---|---|---|
5900f50c1000cf542c51001e | 5 | Problem 415: Titanic sets |
Description
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.
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.
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.
Find T(1011) mod 108.
Instructions
Tests
tests:
- text: <code>euler415()</code> should return 55859742.
testString: assert.strictEqual(euler415(), 55859742, '<code>euler415()</code> should return 55859742.');
Challenge Seed
function euler415() {
// Good luck!
return true;
}
euler415();
Solution
// solution required