C语言题有一个数学等式：AB*CD=BA*DC，式中的一个字母代表一位数字的答案 35、有一个数学等式:AB*CD=BA*DC,式中的一个字母...
python\u8bed\u8a00\u9898\u6709\u4e00\u4e2a\u6570\u5b66\u7b49\u5f0f\uff1aAB*CD=BA*DC\uff0c\u5f0f\u4e2d\u7684\u4e00\u4e2a\u5b57\u6bcd\u4ee3\u8868\u4e00\u4f4d\u6570\u5b57\u7684\u7b54\u6848\uff1ffor A in range(1,10): for B in range(1,10): for C in range(1,10): for D in range(1,10): if A != B != C !=D and B != D != A != C: p1 = A * 10 + B p2 = C * 10 + D q1 = B * 10 + A q2 = D * 10 + C if p1 * p2 == q1 * q2: print([A,B,C,D])
\u7a0b\u5e8f\u7f29\u8fdb\u5982\u56fe\u6240\u793a
\u8fd0\u7b97\u7ed3\u679c\u5982\u56fe\u6240\u793a
AB\u3001BA\u3001CD\u3001DC\u5f0f\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5b57\u6bcd\u4ee3\u8868\u4e00\u4f4d\u6570\u5b57\uff0c\u90a3\u4e48\uff1a
AB=10A+B
BA=10B+A
CD=10C+D
DC=10D+C
AB*CD=(10A+B)*(10C+D)=100A*C+10B*C+10A*D+B*D
BA*DC=(10B+A)*(10D+C)=100B*D+10B*C+10A*D+A*C
\u2235AB*CD=BA*DC
\u5373\uff1a100A*C+10B*C+10A*D+B*D=100B*D+10B*C+10A*D+A*C
\u2234A*C=B*D \uff08A\u3001B\u3001C\u3001D\u4e2d\u4e0d\u5305\u542b0\uff0c\u4e14\u4e92\u4e0d\u76f8\u540c\uff09
1~9\u6570\u5b57\u4e2d\u6ee1\u8db3\u4e0a\u8ff0\u7b49\u5f0f\u7684\u6709\uff1a
1*6=2*3
1*8=2*4
2*6=3*4
2*9=3*6
3*8=4*6
\u4ee5\u4e0a\u4e58\u5f0f\u4e2d2\u56e0\u6570\u53ef\u4e92\u6362\u3002
\u56e0\u6b64\uff0c\u6240\u6709\u7b26\u5408\u8981\u6c42\u7684\u6570\u5bf9\u4e3a\uff1a
A=1,B=2\uff0cC=6,D=3;
A=1,B=3\uff0cC=6,D=2;
A=6,B=2\uff0cC=1,D=3;
A=6,B=3\uff0cC=1,D=2;
......
\u5176\u4f59\u6570\u5bf9\u53ef\u4ee5\u6b64\u7c7b\u63a8\u5199\u51fa\u3002(\u517120\u79cd\u60c5\u5f62\uff0c\u5077\u4e0b\u61d2\uff0c\u5c31\u4e0d\u9010\u4e00\u5217\u51fa\u4e86)
\u793a\u4f8b\uff1a
\u53d6A=1,B=2\uff0cC=6,D=3\uff0c\u6709\uff1a
12*63=756\uff0c21*36=756 \u6ee1\u8db3\u9898\u76ee\u8981\u6c42
\u53d6A=1,B=3\uff0cC=6,D=2\uff0c\u6709\uff1a
13*62=806\uff0c31*26=806 \u6ee1\u8db3\u9898\u76ee\u8981\u6c42
\u53d6A=6,B=2\uff0cC=1,D=3\uff0c\u6709\uff1a
62*13=806\uff0c26*31=806 \u6ee1\u8db3\u9898\u76ee\u8981\u6c42
\u53d6A=6,B=3\uff0cC=1,D=2\uff0c\u6709\uff1a
63*12=756,36*21=756 \u6ee1\u8db3\u9898\u76ee\u8981\u6c42
A = 1 B = 2 C = 6 D = 3
A = 1 B = 2 C = 8 D = 4
A = 1 B = 3 C = 6 D = 2
A = 1 B = 4 C = 8 D = 2
A = 2 B = 1 C = 3 D = 6
A = 2 B = 1 C = 4 D = 8
A = 2 B = 3 C = 6 D = 4
A = 2 B = 3 C = 9 D = 6
A = 2 B = 4 C = 6 D = 3
A = 2 B = 6 C = 3 D = 1
A = 2 B = 6 C = 9 D = 3
A = 2 B = 8 C = 4 D = 1
A = 3 B = 1 C = 2 D = 6
A = 3 B = 2 C = 4 D = 6
A = 3 B = 2 C = 6 D = 9
A = 3 B = 4 C = 8 D = 6
A = 3 B = 6 C = 2 D = 1
A = 3 B = 6 C = 4 D = 2
A = 3 B = 6 C = 8 D = 4
A = 3 B = 9 C = 6 D = 2
A = 4 B = 1 C = 2 D = 8
A = 4 B = 2 C = 3 D = 6
A = 4 B = 3 C = 6 D = 8
A = 4 B = 6 C = 3 D = 2
A = 4 B = 8 C = 2 D = 1
A = 4 B = 8 C = 6 D = 3
A = 6 B = 2 C = 1 D = 3
A = 6 B = 2 C = 3 D = 9
A = 6 B = 3 C = 1 D = 2
A = 6 B = 3 C = 2 D = 4
A = 6 B = 3 C = 4 D = 8
A = 6 B = 4 C = 2 D = 3
A = 6 B = 8 C = 4 D = 3
A = 6 B = 9 C = 3 D = 2
A = 8 B = 2 C = 1 D = 4
A = 8 B = 4 C = 1 D = 2
A = 8 B = 4 C = 3 D = 6
A = 8 B = 6 C = 3 D = 4
A = 9 B = 3 C = 2 D = 6
A = 9 B = 6 C = 2 D = 3
你是要程序吗？我以为只是要答案呢。c++程序如下：
#include <iostream>
#include <fstream>
using namespace std;
int main()
{
int i, j, m, n;
fstream outFile("a.txt", ios::out);
for (i = 0; i<=9; i++)
for (j = 0; j<=9; j++)
for (m = 0; m<=9;m++)
for (n = 0; n<=9; n++)
{
if (i!=j && i!=m && i!=n && j!=m && j!=n && m!=n)
{
if ((i*10+j) * (m*10+n) == (j*10+i) * (n*10+m))
{
cout << "A = " << i << " "
<< "B = " << j << " "
<< "C = " << m << " "
<< "D = " << n << endl;
outFile << "A = " << i << " " //写入文件
<< "B = " << j << " "
<< "C = " << m << " "
<< "D = " << n << endl;
}
}
}
return 0;
}
#include <stdio.h>
void main()
{
int a,b,c,d;
for(a=0; a<=9; a++)
for(b=0; b<=9; b++)
for(c=0; c<=9; c++)
for(d=0; d<=9; d++)
{
if((a*10+b)*(c*10+d)==(10*b+a)*(10*d+c))
if((a!=b)&&(a!=c)&&(a!=d)&&(b!=c)&&(b!=d)&&(c!=d))
printf("\n%d%d*%d%d=%d%d*%d%d",a,b,c,d,b,a,d,c);
}
}
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