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<H1>[Mageia-discuss] Randomised game position (was: Mageia 2 Wireless LAN (Wifi) Connection Keeps Getting Disconnected)</H1>
<B>Deri James</B>
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TITLE="[Mageia-discuss] Randomised game position (was: Mageia 2 Wireless LAN (Wifi) Connection Keeps Getting Disconnected)">deri at chuzzlewit.myzen.co.uk
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<I>Fri Aug 10 11:37:28 CEST 2012</I>
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<PRE>On Friday 10 Aug 2012 09:58:45 RICHARD WALKER wrote:
><i> Do you know those little plastic squares with 24 alphabet tiles in a
</I>><i> 5x5 grid? The idea is to push the tiles around until you have them in
</I>><i> alphabetic order left to right, top to bottom, with an empty square in
</I>><i> the bottom right corner.
</I>><i>
</I>><i> Back in the mid-eighties I wrote a version of this game for my
</I>><i> Sinclair QL. I stored the tiles in a one-dimension array where they
</I>><i> were initially shuffled.
</I>><i>
</I>><i> I discovered, after much trial and error, that the chances of being
</I>><i> able to solve the puzzle after shuffling is almost exactly 1 in 2. The
</I>><i> problem is that 50% of shuffles results in an order where, by the
</I>><i> rules of tile movement, two adjacent tiles must be exchanged - and
</I>><i> that is not possible.
</I>><i>
</I>><i> Any ideas how to test the shuffled result to determine if such a
</I>><i> transposition exists without solving the game?
</I>><i>
</I>
One solution is not to randomise the array, but start from the solved position
and do 50 random (but legal) moves. This will leave a position from which you
can guarantee there is at least one solution (the reverse of the 50 random
moves).
Cheers
Deri
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