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
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.)

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

29922993299429952996299729982999

题目分析

一个四位数,写成十进制,十二进制,十六进制的数值时,三种方式的数值之和相同

如2992(10)=1894(12)=BB0(16)=22

#include <stdio.h>

int sum(int digit, int scale) {
int ans = 0;
while (digit != 0) {
int temp = digit % scale;
ans += temp;
digit = (digit - temp) / scale;
}
return ans;
}

int main()
{
for (int i = 1000; i <= 9999; ++i) {
int a = sum(i, 10);
int b = sum(i, 12);
if (a == b) {
int c = sum(i, 16);
if (b == c)
printf("%d\n", i);
}
}
}