RE: Scramble puzzle

[Stephen Tavener <stephen.tavener@bbc.co.uk>]

Almost certainly impossible.  For most letters of the alphabet, there are
two letter words that both begin and end with that letter... without
reference to an official dictionary, I can think of:

P(A)T		O(B)E		?(C)H		A(D)O		B(E)N
O(F)A
?(G)I		A(H)O		P(I)T		?(J)O		O(K)O
E(L)A
E(M)E		E(N)O		T(O)R		U(P)A		?(Q)I
O(R)E
A(S)O		A(T)O		M(U)P		?(V)?		O(W)E
E(X)I
O(Y)E		?(Z)O

... so if you have an empty space that is in front of only one letter, that
letter has to be one of : C(2),G(4?),J(1),Q(1),V(4?),Z(1)
Similarly, an empty space *after* a letter has to be a 'V'(4?).  So, at most
17 spaces on the board can be adjacent to only one tile.

... which is not a lot of empty space.  This rules out having all the tiles
in a 10x10 grid in the corner even if that were possible, so the tiles must
be spread out to occupy the whole board in such a way that no more than 17
spaces are adjacent to only one tile.

Given that the board contains 225 spaces, and 99 *connected* letters, I
doubt it's possible... let's see:

Number of empty spaces on the board will be 225-99 = 126.
17 of these spaces may be adjacent to exactly one tile, the other 109 must
be adjacent to 2 or more tiles.  109x2+17 = 245.

First tile down, spreads its miasma over 4 empty spaces.  Each subsequent
tile, removes one from the miasma value of the tile it's played against, and
adds 3 miasma of its own, so a net increase of 2 miasma.  So, theoretical
maximum miasma is 4+98x2 = 200.  This is less than the 245 miasma required,
so it's not possible.

TTFN,





Stephen Tavener
DigiText Programmer, BBC News, New Media.

Xtn: 58349/64727
Room 3225, Television Centre, Wood Lane, London. W12 7RJ
mailto:Stephen.Tavener@bbc.co.uk (Work)




-----Original Message-----
From: Cameron Browne [mailto:browne@research.canon.com.au] 
Sent: 05 April 2002 03:02
To: pbmserv-users@gamerz.net
Subject: Scramble puzzle


Does anyone know if it's possible to fit 99 tiles on the Scramble board, 
forming legitimate words in accordance with the rules of Scramble, such 
that the 1 remaining tile *cannont* be placed anywhere on the board?

The 1 remaining tile must be treated as a blank, ie if any letter fits on 
the saturated board then it becomes that letter.


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