perplexus.info :: Numbers : Child Play..

Child Play.. (Posted on 2009-08-07)

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.

Submitted by brianjn

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Solution: (Hide)

Pr Tri Squ Fib 8-digit 23 351 169 987 23516987 31 105 529 987 31052987 41 105 529 987 41052987 43 325 576 610 43257610 43 351 169 987 43516987 61 105 529 987 61052987 ** Originally left out. 83 325 576 610 83257610
The lowest solution terminates in the higher available Fibonacci number while the highest terminates in the lower.

Had I realised at the time of writing the value inadvertently omitted is probably more significant in that its first three digits are the lower Fibonacci value required to satisfy the FGH requirement while the number ends in the higher Fibonacci.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-03-18 00:16:05
re: official solution	brianjn	2009-08-13 00:02:59
official solution	Charlie	2009-08-12 18:08:42
Significance - apology	brianjn	2009-08-10 04:48:04
an answer	Dej Mar	2009-08-08 02:55:38
Signifiers??	ed bottemiller	2009-08-07 15:05:26
re: computer solution -- whoops!	Charlie	2009-08-07 14:05:19
computer solution	Charlie	2009-08-07 13:55:09
Significance	ed bottemiller	2009-08-07 13:53:39
Sets	ed bottemiller	2009-08-07 13:23:34

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