Tetris pieces in a 4x5 grid .. no solution?
Tom Robinson
fit them into a 4x5 grid. Each piece is made up of 4 squares so the
total area is the same. (The line, the T, the S, the square block and
the L). I think I've successfully proved there's no solution, but I'm
told there is one. It must be something sneaky. :) Anyone seen this
one before?
--
Tom Robinson
t.rob...@nospam.net.ntl.com - you know what to do.
http://mystican.dhs.org || pgp: 0xB07F896B
Nick Wedd
<t.rob...@net.ntl.com> writes
>Take all five tetris pieces (ignore the ones which can be flipped) and
>fit them into a 4x5 grid. Each piece is made up of 4 squares so the
>total area is the same. (The line, the T, the S, the square block and
>the L). I think I've successfully proved there's no solution, but I'm
>told there is one. It must be something sneaky. :) Anyone seen this
>one before?
It is not possible.
Proof:
Colour the 4x5 grid like a chess board. Four of the pieces must cover
two black and two white squares, but the T-piece must cover three black
and one white, or the other way round. So you cannot arrange to cover
the 10 black and 10 white squares on the grid.
Nick
--
Nick Wedd ni...@maproom.co.uk
Wei-Hwa Huang
>In article <wxdFOCJKsZj0Ko...@4ax.com>, Tom Robinson
><t.rob...@net.ntl.com> writes
>>Take all five tetris pieces (ignore the ones which can be flipped) and
>>fit them into a 4x5 grid. Each piece is made up of 4 squares so the
>>total area is the same. (The line, the T, the S, the square block and
>>the L). I think I've successfully proved there's no solution, but I'm
>>told there is one. It must be something sneaky. :) Anyone seen this
>>one before?
>It is not possible.
True indeed. A similar puzzle that does have a solution exists --
replace the T shape with another L shape.
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
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"May cause increased occurences of urination when taken with water."
Parallax
<t.rob...@net.ntl.com> wrote:
>Take all five tetris pieces (ignore the ones which can be flipped) and
>fit them into a 4x5 grid. Each piece is made up of 4 squares so the
>total area is the same. (The line, the T, the S, the square block and
>the L). I think I've successfully proved there's no solution, but I'm
>told there is one. It must be something sneaky. :) Anyone seen this
>one before?
<spoiler>
Throw out the line and make the problem getting a 4x4 with the
squiggle, T, L, and box.
The box can't go in the middle, nor can it go on an edge (Because the
L piece would be needed on each side, and you only have 1). So, it
must go in a corner.
Now we need to make an L-shaped 4x4 piece out of the remaining 3
blocks.
+-+-+
|*|*|
+-+-+
|*| |
+-+-+-+-+
|*| | |*|
+-+-+-+-+
| |*|*|*|
+-+-+-+-+
You need the use the L-shaped piece in one of the starred positions,
because neither of the remaining 2 pieces will fit in there without
leaving a hole (Try it and see).
Once you use the L piece in one of the sides, you have the problem on
the other side that no piece will fit.
Can't be done.
--Parallax
Bixente
Tom Robinson <t.rob...@net.ntl.com> wrote in message
news:wxdFOCJKsZj0Ko...@4ax.com...
> Take all five tetris pieces (ignore the ones which can be
flipped) and
> fit them into a 4x5 grid. Each piece is made up of 4
squares so the
> total area is the same. (The line, the T, the S, the
square block and
> the L). I think I've successfully proved there's no
solution, but I'm
> told there is one. It must be something sneaky. :)
Anyone seen this
> one before?
>
> Tom Robinson
> t.rob...@nospam.net.ntl.com - you know what to do.
> http://mystican.dhs.org || pgp: 0xB07F896B
someone's having you on - it cant be done
a fourxfive grid has the same number black squares as
white - the five pieces do not.
the t shape has 3 and 1 while the others are 2 and 2 ( thus
you end up with 11 one colour and 9 the other). you may be
familiar with the game of covering two squares at diagonal
corners of a chess board and then challenging someone to
cover the remaining 62 squares with dominoes. this also
cannot be done for very similar reasons
regards
bixente
Glenn
>Take all five tetris pieces (ignore the ones which can be flipped) and
>fit them into a 4x5 grid. Each piece is made up of 4 squares so the
>total area is the same. (The line, the T, the S, the square block and
>the L). I think I've successfully proved there's no solution, but I'm
>told there is one. It must be something sneaky. :) Anyone seen this
>one before?
It's well known that there is no solution.
Proof:
Color the squares of the 4x5 grid like a checkerboard.
There are 10 black squares and 10 red squares.
Every possible placement of each of the line, the S, the square,
and the L takes up 2 black and 2 red squares. Thus, placing
these pieces leaves 2 black and 2 red squares to be covered
by the T. This is impossible as any placement of the T covers
either 1 black and 3 read or 3 black and 1 red.
This has been known since at least the late 50s. In puzzledom, these
pieces are commonly known at the tetrominoes (all distinct shapes
that can be formed by joining 4 unit squares along their edges).
Patrick Hamlyn
>>It is not possible.
>
>True indeed. A similar puzzle that does have a solution exists --
>replace the T shape with another L shape.
Alternately, replace either the square or the S shape with another T shape.
And while you're at it, find solutions for:
OOTTL
OOSLL
OOLLI
OTTLL
OTTLI
OSLLI
OLLII
TTSSL
TTSLL
TTSLI
TTSII
TTLII
SSLLI
SLLII
(O is the square)
Tom Robinson
proofs. :)