1.1 KiB
id, title, challengeType, forumTopicId
| id | title | challengeType | forumTopicId |
|---|---|---|---|
| 5900f51a1000cf542c51002d | Problem 430: Range flips | 5 | 302101 |
--description--
N disks are placed in a row, indexed 1 to N from left to right.
Each disk has a black side and white side. Initially all disks show their white side.
At each turn, two, not necessarily distinct, integers A and B between 1 and N (inclusive) are chosen uniformly at random. All disks with an index from A to B (inclusive) are flipped.
The following example shows the case N = 8. At the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6.
Let E(N, M) be the expected number of disks that show their white side after M turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.
Find E(1010, 4000). Give your answer rounded to 2 decimal places behind the decimal point.
--hints--
euler430() should return 5000624921.38.
assert.strictEqual(euler430(), 5000624921.38);
--seed--
--seed-contents--
function euler430() {
return true;
}
euler430();
--solutions--
// solution required