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.

(In reply to Part 1 solution by Dej Mar)

I've been struggling to get a total below 500 for this, but your list has given me some clues, and it's now down to 489..

First swap your (second!) 45 for 46.
Then exchange the 22 and 36 for just 26. That gets the right number of each digit, and produces the following list:

{1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,21,23,24,25,26,27,33,34,35,45,46}

Total 489, but I'm not sure it's the lowest possible.

Posted by Harry on 2009-07-11 18:47:37