Sicily 1014. Specialized Four-Dig

1014. Specialized Four-Dig

Constraints

Time Limit: 1 secs, Memory Limit: 32 MB

Description

Find and list all four-digit numbers in decimal notation that have the property that the sum of its four digits equals the sum of its digits when represented in hexadecimal (base 16) notation andalso equals the sum of its digits when represented in duodecimal (base 12) notation.

 

For example, the number 2991 has the sum of (decimal) digits 2+9+9+1 = 21.  Since 2991 = 1*1728 + 8*144 + 9*12 + 3, its duodecimal representation is 189312, and these digits also sum up to 21.  But in hexadecimal 2991 is BAF16, and 11+10+15 = 36, so 2991 should be rejected by your program.

 

The next number (2992), however, has digits that sum to 22 in all three representations (including BB016), so 2992 should be on the listed output.  (We don’t want decimal numbers with fewer than four digits — excluding leading zeroes — so that 2992 is the first correct answer.)

Input

There is no input for this problem

Output

Your output is to be 2992 and all larger four-digit numbers that satisfy the requirements (in strictly increasing order), each on a separate line with no leading or trailing blanks, ending with a new-line character. There are to be no blank lines in the output. The first few lines of the output are shown below.

Sample Input

There is no input for this problem

Sample Output

2992

2993

2994

2995

2996

2997

2998

2999

这道题的题意就是给出一个数字，把它转化成12进制，16进制，以及他自身这三个数字的各个位置加起来的和相同，如题目中给的2992，这道题的思路就是把一个数字转化成12进制及16进制，然后把它的各个位相加，核心代码如下

分别是把一个数字转化成10.12.16进制之后各个位的和，对数字A进行判断，若dec(A),twelve(A),hex(A)两两相等，则将其输出

#include<iostream>
using namespace std;
int dec(int n){
	int sum=0;
	while(n!=0){
		sum+=(n%10);
		n/=10;
	}
	return sum;
}
int twelve(int n){
	int sum=0;
	while(n!=0){
		sum+=(n%12);
		n/=12;
	}
	return sum;
}
int hex(int n){
	int sum=0;
	while(n!=0){
		sum+=(n%16);
		n/=16;
	}
	return sum;
}
int main(){
	for(int i=2992;i<=9999;i++){
		if(dec(i)==hex(i)&&dec(i)==twelve(i)){
			cout<<i<<endl;
		}
	}
}