111111111....or maybe not! *

A version of "hopscotch" has this layout:

			D		G
A	B	C		F
			E		H

Replace each of the letters with a unique digit from 0 to 9 such that you "hop" from one criterion to the next:
11111 AB is Prime,
11111 BCD is a Triangle,
11111 DEF is a Square and
11111 FGH is a Fibonacci number,
111111111111111 and none begin with a zero.

What 8-digit numbers are formed by this process?
What is significant about the highest and lowest?

* This can be logically deduced albeit a little time consuming.

It does not seem very exciting, as to "significance", but the lowest and highest do not share any of the four substrings with each other.  The second, third, and fifth share all except the leading prime. (I assume the proposer asks for some property which the highest and lowest share, which does not obtain for the other sets. -- ??).

Posted by ed bottemiller on 2009-08-07 13:53:39