[Jprogramming] Setless SET

[Norman Thomson]

Micke,
Thanks very much for pointing me to the website which certainly makes
things unambiguous.  And Roger, I took a slightly different line to you,
but I am still a million miles away from counting the number of setless
collections of 20 cards.  For what it's worth, my ideas are based on the
fact that any two cards define a set-completing third card.  That means
that for a given collection of 20 it isn't intolerable to get the 190
possible completers and see if they are anywhere in the collection.  I
have just done this 5000 times for collections of 20 and still haven't
found a setless one.  My feeling is that they must be pretty rare, but I
haven't the time left to go 20!81=10^18 times round the loop!  Have you
(or anyone else) solved the problem?  I would be intrigued to know how.  

Best Wishes,
Norman.

   com2=.($:@<: , (,.~ i.)@<:)`(0: , 1:)@.(=&2)  NB. all combinationss of
2 from n
   com2 3
0 1
0 2
1 2 
    comp=.3&-@:+`[@.=/&>	NB. completes 3rd member of set  
    0 1 1 2 comp 2 1 0 0	
1 1 2 1
   hasset=.+./@(e.~comp/"2@({~com2@#))     NB. 1 if set is in y.
   hasset ?20 4$3 	NB. test random set of 20 cards