% Lecture #1: Enumeration
% Farkle Odds
% p(3 of a kind)
% xxx a b c
% xxx aa b
tic
Pair3 = 0;

for d1 = 1:6
   for d2 = 1:6
      for d3 = 1:6
         for d4 = 1:6
            for d5 = 1:6
               for d6 = 1:6
                   Dice = [d1,d2,d3,d4,d5,d6];
                   % check for pairs
                   N = zeros(1,6);
                   for i=1:6
                      for j=1:6
                         if(Dice(j) == i)
                            N(i) = N(i) + 1;
                         end
                      end
                   end
                   [N,b] = sort(N, 'descend');
                   if ( (N(1) == 3) & (N(4) < 3)) 
                      Pair3 = Pair3 + 1;
                   end
               end
            end
         end
      end
   end
end

% probability:
disp('3 of a kind odds')
Pair3
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