#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; const int INF = 1e9; const ll LINF = 1e18; template ostream& operator << (ostream& out,const pair& o){ out << "(" << o.first << "," << o.second << ")"; return out; } template ostream& operator << (ostream& out,const vector V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; } template ostream& operator << (ostream& out,const vector > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; } template ostream& operator << (ostream& out,const map mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; } /* 問題文============================================================ 1個のサイコロを何回か振って目の合計をK以上にしたい。 サイコロを振る回数の期待値を求めよ。 なお、今回のサイコロの場合に回数の期待値(E(x)の公式は以下であることが知られている E(x) := これまでの目の合計が x のとき、合計が K に達するまでにあと振ることになる回数の期待値 E(x)=E(x+1)∗1/6+E(x+2)∗1/6+E(x+3)∗1/6+E(x+4)∗1/6+E(x+5)∗1/6+E(x+6)∗1/6+1 ================================================================= 解説============================================================= ================================================================ */ double E(ll x,ll K){ if(x >= K) return 0.; double res = 0.0; for(ll a = 1; a <=6; a++){ res += E(x+a,K)/6.; } res += 1.; return res; } double solve(){ double res = 0; ll K; cin >> K; res = E(0,K); return res; } int main(void) { cin.tie(0); ios_base::sync_with_stdio(false); cout << fixed << solve() << endl; return 0; }