#include #include #include #include using namespace std; int main() { int k; cin >> k; // [n][k]: n回目で合計をkにできる場合の数 vector > patterns(1 + k, vector(1 + k * 6)); patterns[0][0] = 1; for (int n = 1; n <= k; ++n) { for (int m = 1; m <= k * 6; ++m) { patterns[n][m] = 0; for (int i = 1; i <= 6; ++i) { if (m - i >= 0) { patterns[n][m] += patterns[n - 1][m - i]; } } } } // [n][k]: n回振ったとき合計がkになる確率 vector > pSumEquals(1 + k, vector(1 + k * 6)); for (int n = 0; n <= k; ++n) { for (int m = 0; m <= k * 6; ++m) { pSumEquals[n][m] = patterns[n][m] * pow(1. / 6., n); } } // [n][k]: n回振ったとき合計がk以上になる確率 vector > pSumGreater(1 + k, vector(1 + k * 6)); for (int n = 0; n <= k; ++n) { for (int m = 0; m <= k * 6; ++m) { pSumGreater[n][m] = 0; for (int i = m; i <= k * 6; ++i) { pSumGreater[n][m] += pSumEquals[n][i]; } } } // [n][k]: n-1回目で合計がk未満であり、n回目で合計がkを超える確率 vector > pSumOver(1 + k, vector(1 + k * 6)); for (int n = 1; n <= k; ++n) { for (int m = 0; m <= k * 6; ++m) { pSumOver[n][m] = 0; for (int i = 0; i <= m - 1; ++i) { if (m + 1 - i >= 0 && m + 1 - i < 1 + k * 6) { pSumOver[n][m] += pSumEquals[n - 1][i] * pSumGreater[1][m + 1 - i]; } } } } double lower = 0; double upper = k * 6; while (upper - lower > 1E-5) { double e = (lower + upper) / 2; double solution = 0; for (int i = 1; i <= k; ++i) { solution += i * pSumEquals[i][k]; } for (int i = 1; i <= k; ++i) { solution += (i + e) * pSumOver[i][k]; } solution -= e; if (solution > 0.0) { lower = e; } else { upper = e; } } cout << fixed << setprecision(4) << lower << endl; return 0; }