freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-423-consecutive-die-throws.md

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:

$$\begin{align} & (\underline{1}, \underline{1}, 5, 6, 6, 6, 3) \\ & (1, 1, 5, \underline{6}, \underline{6}, 6, 3) \\ & (1, 1, 5, 6, \underline{6}, \underline{6}, 3) \end{align}$$

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) = 361\\,912\\,500 and C(24) = 4\\,727\\,547\\,363\\,281\\,250\\,000.

Define S(L) as \sum C(n) for 1 ≤ n ≤ L.

For example, S(50)\bmod 1\\,000\\,000\\,007 = 832\\,833\\,871.

Find S(50\\,000\\,000)\bmod 1\\,000\\,000\\,007.

¹ π denotes the prime-counting function, i.e. π(n) is the number of primes ≤ n.

--hints--

consecutiveDieThrows() should return 653972374.

assert.strictEqual(consecutiveDieThrows(), 653972374);

--seed--

--seed-contents--

function consecutiveDieThrows() {

  return true;
}

consecutiveDieThrows();

--solutions--

// solution required