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### Arranging Numbers

```Date: 06/26/2002 at 18:22:09
From: Rhonda Johnson
Subject: Math using tile numbers

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, and 8 in this format:

? ?
? ? ? ?
? ?

Consecutive numbers can't be adjacent vertically, horizontally, or
diagonally.  Use only the numbers given.  For example, the arrangement

1 5
4 7 3 6
2 8

cannot be a solution because the 5 and 6 are adjacent
diagonally, as are the numbers 2 and 3.

```

```
Date: 06/26/2002 at 20:06:22
From: Doctor Greenie
Subject: Re: Math using tile numbers

Hi, Rhonda --

This is a great puzzle in logic....!

I would like to just suggest something for you to think about to get
started on this puzzle - to see if you can follow that suggestion
through to the solution.  This puzzle is so much more satisfying when
you solve at least part of it on your own, rather than having
somebody show you the solution.

Let's start by labeling the positions as follows:

A  B
C  D  E  F
G  H

The keys to the solution are positions D and E.  Position D is
adjacent either vertically, horizontally, or diagonally, to all other
positions except position F; position E is adjacent either
vertically, horizontally, or diagonally, to all other positions
except position C.

Now think carefully about how many numbers are adjacent to each of
the numbers you have to work with.  For example, there are two
numbers adjacent to 3 (i.e., 2 and 4); there are also two numbers
adjacent to 7 (i.e., 6 and 8).  But there is only one number adjacent
to 1 (i.e., 2); and there is only one number adjacent to 8 (i.e., 7).

Putting the ideas of the preceding two paragraphs together tells you
which numbers must go in positions D and E; once you have those
numbers in place, the numbers in positions C and F are uniquely
determined by the requirements of the problem; and then the rest of
the solution is fairly easy.

Good luck with this!  Write back if you have any further questions on
this... but please make an effort to finish the problem yourself
before you write back.

(Or, it would be great to hear back from you if my help enabled you
to find the solution...!)

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logic
High School Puzzles
Middle School Logic
Middle School Puzzles

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