1.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f48a1000cf542c50ff9c | Problem 285: Pythagorean odds | 5 | 301936 | problem-285-pythagorean-odds |
--description--
Albert chooses a positive integer k, then two real numbers a, b are randomly chosen in the interval [0,1] with uniform distribution.
The square root of the sum (k·a+1)2 + (k·b+1)2 is then computed and rounded to the nearest integer. If the result is equal to k, he scores k points; otherwise he scores nothing.
For example, if k = 6, a = 0.2 and b = 0.85, then (k·a+1)2 + (k·b+1)2 = 42.05. The square root of 42.05 is 6.484... and when rounded to the nearest integer, it becomes 6. This is equal to k, so he scores 6 points.
It can be shown that if he plays 10 turns with k = 1, k = 2, ..., k = 10, the expected value of his total score, rounded to five decimal places, is 10.20914.
If he plays 105 turns with k = 1, k = 2, k = 3, ..., k = 105, what is the expected value of his total score, rounded to five decimal places?
--hints--
euler285()
should return 157055.80999.
assert.strictEqual(euler285(), 157055.80999);
--seed--
--seed-contents--
function euler285() {
return true;
}
euler285();
--solutions--
// solution required