题目205：骰子游戏

欧拉计划

Dice Game

Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4.
Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.

Peter and Colin roll their dice and compare totals: the highest total wins. The result is a draw if the totals are equal.

What is the probability that Pyramidal Pete beats Cubic Colin? Give your answer rounded to seven decimal places in the form 0.abcdefg.

题目：

Peter 有九个四面的（金字塔型）骰子，每个分别标上 1，2，3，4。
Colin 有六个六面（正方体）骰子，每个分别标上 1，2，3，4，5，6。

Peter 和 Colin 摇骰子，然后比较他们得到的总和：总和最高的获胜。如果相等的话，则是平局。
请问，金字塔 Peter 赢了正方体 Colin 的概率是多少？以七位小数 0.abcdefg 的形式给出你的答案。

fc1735

#include<stdio.h>

#define SIZE 36

#define fun(x,y,z) \
for(int i##x=1;i##x<=y;i##x++){\
        z;\
}

int main()
{
        int pyram[SIZE+1]={0,};
        int cubic[SIZE+1]={0,};
        fun(1,4,fun(2,4,fun(3,4,fun(4,4,fun(5,4,fun(6,4,fun(7,4,fun(8,4,fun(9,4,pyram[i1+i2+i3+i4+i5+i6+i7+i8+i9]++;)))))))));
        fun(1,6,fun(2,6,fun(3,6,fun(4,6,fun(5,6,fun(6,6,cubic[i1+i2+i3+i4+i5+i6]++;))))));

        for(int i=1;i<=SIZE;i++)
                cubic[i]+=cubic[i-1];
        long total=0;
        for(int i=SIZE;i;i--)
                total+=(long)pyram[i]*cubic[i-1];
        long double rate=total;
        fun(0,6,rate/=6);
        fun(0,9,rate/=4);

        printf("%.7Lf\n",rate);

}

simple brute force