Subject: Re: Sequencing integers
Date: Sun, 18 Jan 1998 13:36:59 -0500
From: Alex Bogomolny
Come to think of it.
Drop the nine multiples of ten: 10, 20, 30, ... The integers that remain may be looked at as domino pieces. It's a good but not difficult problem to show that however you place them back-to-back according to the domino rules, you'll be always able to place all of them. So, you may think of how to place them to get a smallest possible number. Note that the length of the string does not depend on the order of pieces.
The moves are forced. For example, the first got to be 11, next should come 12, then, 21, 13, 31, 14, 41, ... You always have to selected the smallest suitable number.
Two steps remain:
- We have to place the tens: 10, 20 , 30, ...
- We have to coalesce repeated digits.
Give a little thought to how to proceed. I'd be grateful to hear of your solution.