
!24Tiles          E.T.Emms
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   Consider a square tile divided into 4 by the two diagonals. We
may colour these 4 parts using a selection from three colours, say
red,white and blue. If we make all the distinguishable tiles (they
can be rotated biut not turned over) we find that there are just
24 of these tiles. The problem is to put these tiles into a 4x6
rectangle such that a0 where tiles touch they share the same
colour b) the border is all the same colour (the display will
nominate the colour). We first nominate a square on the board
where we wish to place a tile by clicking on it (it turns green).
You can change your mind and click on another square. Then you can
choose a tile from the 24 at the top of the display by clicking on
it. It is immediately transferred to the 'hand'. It can be rotated
either way by clicking on the boxes to the left or right of it. By
clicking on the PUT box you can (if the move is legal) place the
tile on the board. An illegal move is signified by the usual beep.
You can change the chosen tile on the hand by clicking on a new
tile in the heap. The new tile will be put on the hand and the old
one transferred back to the top. A tile on the board may be
removed by clicking on it. Clicking on a tile in the hand will
remove it to the top.

!24TArc1 and !24TArc2
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    These are two programs to solve the !24Tiles problem. It has
been observed (I have never seen a proof) that in every solution
there is a 'bridge' running vertically in the same colour as the
border. This bridge may be in columns 2,3,4 or5. !24Arc1 finds
solutions with the bridge in column 2 (and by symmetry covers
column 5) and !24Arc2 finds solutions in column 3 (covering 4).
This is a difficult problem involving much computing so there may
be big time gaps between solutions in spite of the speed of the
Archimedes! Each solution is dispayed for a short period before
commencing the search for the next.