Specialized Four-Digit Numbers

Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 6682 Accepted: 4859


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 and also 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.)


There is no input for this problem


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

本题是一道考察进制之间转换算法的题目,可以写一个函数sum(进制, 换算的数值),这样的话就做到的Do Not Repeat Yourself的原则了,这个函数要将所有数值模进制的值加起来返回就行了。
#include <iostream>
#include <stdio.h>
using namespace std;

int sum(int sys, int num)
	int shang = num, mod, sum = 0;
	while (shang) {
		mod = shang % sys;
		sum += mod;
		shang = shang / sys;
	return sum;

int main()
	for (int i = 2992; i < 10000; i++) {
		if (sum(16, i) == sum(10, i) && sum(12, i) == sum(10, i)) {
	return 0;
Result Memory Time Language Code Length
Accepted 232K 0MS C++ 397B


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