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* fix: clean-up Project Euler 281-300 * fix: missing image extension * fix: missing power Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing subscript Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
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id, title, challengeType, forumTopicId, dashedName
| 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 {(ka + 1)}^2 + {(kb + 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 {(ka + 1)}^2 + {(kb + 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, \ldots, k = 10, the expected value of his total score, rounded to five decimal places, is 10.20914.
If he plays {10}^5 turns with k = 1, k = 2, k = 3, \ldots, k = {10}^5, what is the expected value of his total score, rounded to five decimal places?
--hints--
pythagoreanOdds() should return 157055.80999.
assert.strictEqual(pythagoreanOdds(), 157055.80999);
--seed--
--seed-contents--
function pythagoreanOdds() {
return true;
}
pythagoreanOdds();
--solutions--
// solution required