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.

I find six sets which meet the conditions:

2 3 5 1 6 9 8 7

3 1 0 5 2 9 8 7

4 1 0 5 2 9 8 7

4 3 2 5 7 6 1 0

6 1 0 5 2 9 8 7

8 3 2 5 7 6 1 0

The easiest way is to start from the right and work left for possible matches, e.g. only 610 and 987 for FGH.

I'll post this, and then consider what might be considered "significant" about the first and last.

Posted by ed bottemiller on 2009-08-07 13:23:34