本文介绍了一个有趣的数学问题——如何使用1到9这九个数字进行排列组合，使得一个四位数乘以一个一位数的结果仍为四位数，并且所有数字都不重复出现。通过Java程序实现了这一逻辑，详细展示了判断条件及其实现方法。
/**
* 九个数字：
* 功能：实现填充。一个四位数乘以一个一位数，得到一个四位数。这九个数分别用1~9这九个数填充。
*/
public class NineNumbers{
public static void main(String[] args){
int product = 0;
for(int i = 1234; i <= 9876; i++){
if(!theThouthandNumberWithoutSameNumberAndZero(i)){
continue;
}
for(int j = 1; j <= 9; j++){
if(theThouthandNumberWithTheOne(i, j)){
continue;
}
product = i * j;
if(!isThouthandNumber(product)){
continue;
}
if(!theThouthandNumberWithoutSameNumberAndZero(product)){
continue;
}
if(theThouthandNumberWithTheOne(product, j)){
continue;
}
if(theTwoThouthandNumberWithoutSameNumber(i, product)){
System.out.println("^_^ : I know " + i + " * " + j + " = " + product);
}
}
}
}
/**
* 判断一个数是不是一个四位数
*/
public static boolean isThouthandNumber(int number){
int thouthand = number/1000;
if(thouthand > 9 || thouthand < 1){
return false;
}
return true;
}
/**
* 判断四位数里面有没有跟一个一位数相同的数字
*/
public static boolean theThouthandNumberWithTheOne(int thoutandNumber, int one){
int number_thousand = thoutandNumber/1000;
int number_hundred = thoutandNumber%1000/100;
int number_ten = thoutandNumber%100/10;
int number_one = thoutandNumber%10;
if(one == number_thousand || one == number_hundred || one == number_ten || one == number_one){
return true;
}
return false;
}
/**
* 判断两个四位数不含有相同的数字
*/
public static boolean theTwoThouthandNumberWithoutSameNumber(int number1, int number2){
int number1_thousand = number1/1000;
int number1_hundred = number1%1000/100;
int number1_ten = number1%100/10;
int number1_one = number1%10;
int number2_thousand = number2/1000;
int number2_hundred = number2%1000/100;
int number2_ten = number2%100/10;
int number2_one = number2%10;
boolean[] signs = new boolean[10];
signs[number1_thousand] = true;
signs[number1_hundred] = true;
signs[number1_ten] = true;
signs[number1_one] = true;
if(signs[number2_thousand]){
return false;
}
if(signs[number2_hundred]){
return false;
}
if(signs[number2_ten]){
return false;
}
if(signs[number2_one]){
return false;
}
return true;
}
/**
* 判断一个四位数没有相同数字且不含有零
*/
public static boolean theThouthandNumberWithoutSameNumberAndZero(int number){
int number_thousand = number/1000;
int number_hundred = number%1000/100;
int number_ten = number%100/10;
int number_one = number%10;
boolean[] signs = new boolean[10];
signs[number_thousand] = true;
if(!signs[number_hundred]){
signs[number_hundred] = true;
} else {
return false;
}
if(!signs[number_ten]){
signs[number_ten] = true;
} else {
return false;
}
if(!signs[number_one]){
signs[number_one] = true;
} else {
return false;
}
if(signs[0]){
return false;
}
return true;
}
}
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