matches=lettersgame(letters,nletters)

function matches=lettersgame(letters,nletters)
%  function matches=lettersgame(letters,[nletters])
% solves the countdown letters game
% e.g.a=lettersgame('cedeinter')
% the optional argument nletters gives smallest output word size (default is 4)
%
if nargin<2
    nletters=4;                                                     % default smallest word length to return
end
letters=strrep(letters,' ','');                                     % remove any spaces
letters=sort(lower(letters(:)))';                                   % change to sorted lower case and make into row
N=length(letters);
allwords=textread('scrabblewords.txt','%s');                        % read dictionary as a cell array
allwords=char(allwords);                                            % convert to a matrix
allwords=allwords(allwords(:,1)>'Z',:);                             % remove proper nouns
allwords=allwords(allwords(:,N+1)==' ',1:N);                        % remove all words longer than N
for nletters=nletters:N;
    matches{nletters}=[];
% get a smaller dictionary with just nletters letters in each word.
    if nletters<N
        wordsnl=allwords(allwords(:,nletters+1)==' ',1:nletters);   % remove all words longer than nletters
    else
        wordsnl=allwords;
    end
    wordsnl=wordsnl(wordsnl(:,nletters-1)>' ',1:nletters);          % remove all words shorter than nletters
    sortnl=sort(wordsnl')';
    hash=32.^(1:nletters)';
    hashtable=(sortnl-'a')*hash;
    allcombs=nchoosek(letters,nletters);                            % get all combinations of nletter letters from selection
    allcombs=unique(allcombs,'rows');
    for ii=1:size(allcombs,1);                                      % for each letter combination
        combo=allcombs(ii,:)-'a';
% now find the indices of the sorted dictionary that match this sorted combination of letters
        match=find((combo*hash==hashtable));
        matches{nletters}=[matches{nletters}; wordsnl(match,:)];            % store the results
    end
    if nargout==0
        fprintf(' Found %i x %i letters\n',size(matches{nletters},1),nletters)
        if (size(matches{nletters},1)<10) | (nletters>6)
            disp('')
            disp(matches{nletters});
            disp('')
        end
    end
end