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no 4 on a plane (3*3*3 puzzle)
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Torsten Sillke  
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 More options 27 Nov 1992, 15:47
Newsgroups: rec.puzzles
From: sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke)
Date: Fri, 27 Nov 1992 15:25:17 GMT
Local: Fri 27 Nov 1992 15:25
Subject: no 4 on a plane (3*3*3 puzzle)
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On the 2*2*2 grid you can take 5 points, such that no 4 points lay on a
plane. The only possibility (up to symmetry) is:

        o .      . o
        o o      o .

Can you find the only possibility to take 8 points in the 3*3*3 grid
with the same property?

good luck, Torsten Sillke
(as nobody mastered any of the puzzles I posted so far, I hope this is
easy enough for you.)


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Torben AEgidius Mogensen  
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 More options 27 Nov 1992, 17:03
Newsgroups: rec.puzzles
From: torb...@diku.dk (Torben AEgidius Mogensen)
Date: 27 Nov 92 16:16:06 GMT
Local: Fri 27 Nov 1992 16:16
Subject: Re: no 4 on a plane (3*3*3 puzzle)
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sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:
>On the 2*2*2 grid you can take 5 points, such that no 4 points lay on a
>plane. The only possibility (up to symmetry) is:
>        o .      . o
>        o o      o .
>Can you find the only possibility to take 8 points in the 3*3*3 grid
>with the same property?

How about

. o .   o . .   . . o
. . o   . . .   o . .
o . .   . . o   . o .

        Torben Mogensen (torb...@diku.dk)


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der Mouse  
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 More options 28 Nov 1992, 08:41
Newsgroups: rec.puzzles
From: mo...@thunder.mcrcim.mcgill.edu (der Mouse)
Date: 28 Nov 92 08:28:47 GMT
Local: Sat 28 Nov 1992 08:28
Subject: Re: no 4 on a plane (3*3*3 puzzle)
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In article <1992Nov27.161606.1...@odin.diku.dk>, torb...@diku.dk (Torben AEgidius Mogensen) writes:

> sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:
>> On the 2*2*2 grid you can take 5 points, such that no 4 points lay
>> on a plane.  [...]  Can you find the only possibility to take 8
>> points in the 3*3*3 grid with the same property?
> How about
> . x .   x . .   . . o
> . . x   . . .   x . .
> o . .   . . x   . x .

Sorry.  The six (!) points I marked with x are all in the same plane.

                                        der Mouse

                            mo...@larry.mcrcim.mcgill.edu


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David Seal  
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 More options 30 Nov 1992, 23:04
Newsgroups: rec.puzzles
From: ds...@armltd.co.uk (David Seal)
Date: 30 Nov 92 15:31:11 GMT
Local: Mon 30 Nov 1992 15:31
Subject: Re: no 4 on a plane (3*3*3 puzzle)
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In article <1992Nov27.161606.1...@odin.diku.dk> torb...@diku.dk (Torben

AEgidius Mogensen) writes:
>sil...@math25.mathematik.uni-bielefeld.de (Torsten Sillke) writes:
>>Can you find the only possibility to take 8 points in the 3*3*3 grid
>>with the same property?

>How about

>. o .       o . .   . . o
>. . o       . . .   o . .
>o . .       . . o   . o .

No, there's a diagonal plane which passes through no less than 6 of these
points!

. O .   O . .   . . o
. . O   . . .   O . .
o . .   . . O   . O .

The six points marked with upper-case "O"s are coplanar.

David Seal
ds...@armltd.co.uk

All opinions are mine only...


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