* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1.2 KiB
id, title, challengeType, forumTopicId, dashedName
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f5141000cf542c510027 | Problem 423: Consecutive die throws | 5 | 302093 | problem-423-consecutive-die-throws |
--description--
Let n be a positive integer.
A 6-sided die is thrown n times. Let c be the number of pairs of consecutive throws that give the same value.
For example, if n = 7 and the values of the die throws are (1,1,5,6,6,6,3), then the following pairs of consecutive throws give the same value: (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) (1,1,5,6,6,6,3) Therefore, c = 3 for (1,1,5,6,6,6,3).
Define C(n) as the number of outcomes of throwing a 6-sided die n times such that c does not exceed π(n).1 For example, C(3) = 216, C(4) = 1290, C(11) = 361912500 and C(24) = 4727547363281250000.
Define S(L) as ∑ C(n) for 1 ≤ n ≤ L. For example, S(50) mod 1 000 000 007 = 832833871.
Find S(50 000 000) mod 1 000 000 007.
1 π denotes the prime-counting function, i.e. π(n) is the number of primes ≤ n.
--hints--
euler423()
should return 653972374.
assert.strictEqual(euler423(), 653972374);
--seed--
--seed-contents--
function euler423() {
return true;
}
euler423();
--solutions--
// solution required