1.4 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4a81000cf542c50ffbb | Problem 316: Numbers in decimal expansions | 5 | 301972 | problem-316-numbers-in-decimal-expansions |
--description--
Let p = p1 p2 p3 ... be an infinite sequence of random digits, selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
It can be seen that p corresponds to the real number 0.p1 p2 p3 ....
It can also be seen that choosing a random real number from the interval [0,1) is equivalent to choosing an infinite sequence of random digits selected from {0,1,2,3,4,5,6,7,8,9} with equal probability.
For any positive integer n with d decimal digits, let k be the smallest index such that pk, pk+1, ...pk+d-1 are the decimal digits of n, in the same order. Also, let g(n) be the expected value of k; it can be proven that g(n) is always finite and, interestingly, always an integer number.
For example, if n = 535, then for p = 31415926535897...., we get k = 9 for p = 355287143650049560000490848764084685354..., we get k = 36 etc and we find that g(535) = 1008.
Given that , find
Note: represents the floor function.
--hints--
euler316()
should return 542934735751917760.
assert.strictEqual(euler316(), 542934735751917760);
--seed--
--seed-contents--
function euler316() {
return true;
}
euler316();
--solutions--
// solution required