Part 1: Find the smallest set of distinct whole numbers that contains nine 1s, eight 2s, seven 3s, ..., one 9

Part 2: Find the smallest set of distinct whole numbers that contains ten 0s, nine 1s, eight 2s, ..., one 9 (Of course the 0s cannot be leading.)

Smallest refers to the sum of the numbers in the set.

{1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 27, 33, 34, 35, 36, 45, 45} with a sum of 498

One can obtain the same sum by swapping the trailing digits of some of the numbers, e.g., 27 & 36 with 26 & 37 -- therefore, it is possible for more than one solution (assuming the sum I have presented is indeed the lowest possible). 

Edited on July 9, 2009, 1:03 pm

Posted by Dej Mar on 2009-07-09 12:12:03