1064 - Throwing Dice
| PDF (English) | Statistics | Forum |
| Time Limit: 2 second(s) | Memory Limit: 32 MB |
n common cubic dice are thrown. What is the probability that the sum of all thrown dice is at least x?
Input
Input starts with an integer T (≤ 200), denoting the number of test cases.
Each test case contains two integers n (1 ≤ n < 25) and x (0 ≤ x < 150). The meanings of n and x are given in the problem statement.
Output
For each case, output the case number and the probability in 'p/q' form where p and q are relatively prime. If q equals 1 then print p only.
Sample Input |
Output for Sample Input |
| 7 3 9 1 7 24 24 15 76 24 143 23 81 7 38 |
Case 1: 20/27 Case 2: 0 Case 3: 1 Case 4: 11703055/78364164096 Case 5: 25/4738381338321616896 Case 6: 1/2 Case 7: 55/46656 |
/* ***********************************************
Author : ryc
Created Time : 2016-08-25 Thursday
File Name : E:\acm\LightOJ\106.cpp
Language : c++
Copyright 2016 ryc All Rights Reserved
************************************************ */
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;
typedef long long LL;
typedef pair<int,int>pii;
const int maxn=10010;
LL dp[30][155];
int n,m;
LL gcd(LL a,LL b){return b==0?a:gcd(b,a%b);
}
void Find(){dp[0][0]=1ll;for(int i=1;i<=25;++i){for(int j=1;j<=150;++j){for(int k=1;k<=6&&j-k>=0;++k){dp[i][j]+=dp[i-1][j-k];}}}
}
int main()
{Find();int t,T=1;cin>>t;while(t--){scanf("%d%d",&n,&m);LL ans=0,sum=1ll;for(int i=n;i<m;++i){ans+=dp[n][i];}for(int i=1;i<=n;++i){sum*=6ll;}ans=sum-ans;printf("Case %d: ",T++);if(ans==0){printf("0\n");}else {LL g=gcd(ans,sum);if(sum/g==1){printf("%lld\n",ans/g);}else {printf("%lld/%lld\n",ans/g,sum/g);}}}return 0;
}