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.

23516987 : 23 - 351 - 169 - 987 : {0,4} *
31052987 : 31 - 105 - 529 - 987 : {4,6}
41052987 : 41 - 105 - 529 - 987 : {3,6}
43257610 : 43 - 325 - 576 - 610 : {8,9}
43516987 : 43 - 351 - 169 - 987 : {0,2) *
61052987 : 61 - 105 - 529 - 987 : {3,4)
83257610 : 83 - 325 - 576 - 610 : {4,9)

* One aspect of the 8-digit numbers formed is that those missing a 0 in their construction do not 'hopscotch' in increasing numbers (i.e., their square is smaller than their triangular number).  
A 'significant'(?) aspect is that the lowest is missing the lowest decimal digit, 0; the highest is missing the highest decimal digit, 9; and, not as significant, both are missing the decimal digit 4.

Posted by Dej Mar on 2009-08-08 02:55:38