
ZOJ Problem Set  2405
Find and list all fourdigit 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 fourdigit numbers that satisfy the requirements (in strictly increasing order), each on a separate line with no leading or trailing blanks, ending with a newline 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 Source: Pacific Northwest 2004 