2003 => 127 + 172 + 271 + 712 + 721 Also the uniq solutiions.. 5106 == 689 + 698 + 869 + 896 + 968 + 986 5328 == 789 + 798 + 879 + 897 + 978 + 987 Interesting:: 2001,2003,2005,2011,2014,2020 etc.. all are numbers which are sum of numbers with the same digits in a uniq way. I wonder if there's a series for this type of numbers.. A N Kadakia ---------------------------------------------------- Barcelona, Catalonia, 10 d'abril de 2003 127 + 172 + 271 + 712 + 721 = 2003 Jordi Domènech --------------------------------------------------- 127+172+271+712+721=2003 Zbigniew Zarzycki -------------------------------------------- Hello! 2003 = 127 + 172 + 271 + 712 + 721 This wasn't very easy.. Juha Saukkola --------------------------------------- Erich Friedman: It is easy to express 2004 as the sum of distinct positive numbers with the same digits: 2004 = 725 + 752 + 527, 2004 = 617 + 671 + 716, 2004 = 509 + 590 + 905. It is hard to write 2003 as the sum of distinct positive numbers with the same digits. The answer appears to be unique. For the above question.. there is one more answer.. that is 914+941+149 = 2004 -------------------------------------------- A quick analysis shows that 2 and 7 numbers would be too few or too many, respectively, that 3 or 6 wouldn't work because of the property of nines and because 2003 isn't a multiple of 3. The combinations with 4 numbers can be breezed through pretty quickly, which leaves 5 numbers. Since all are the same mod 9, and 5 ÷ 5 = 1 (mod 9), each has to be equivalent to 1 (mod 9). The sum of the digits, then, is most likely 10 (19 seems too high, and 1 is impossibly low). 2003 can be thought of as the six permutations of the three digits added together, minus one of them. In these six, the sum should be 2220 (since the sum of the digits in each place value is 20). 2220 - 2003 = 217. The other five must be: 127 + 172 + 271 + 712 + 721 = 2003 -Jonah Ostroff --------------------------------------------- 127+172+271+712+721=2003 James Lewis Melby ---------------------------------------------- Great problem! My answer is: 127 + 172 + 271 + 712 + 721 = 2003. Peter Exterkate ---------------------------------------------- 271 + 721 + 712 + 127 + 172 - Matt Elder ----------------------------------------------