[Jprogramming] All selected hand possibilities (long)

['Mike Day' via Programming]

NB. No history in this comment - side-effect of using iPad away from home WiFi

My farthingsworth:

Suppose you’ve got one canonical solution in the form of an array of m-hands compatible (in some way) with one canonical n-hand.  (Devon asked for all 5-hands given 1 (or 6 permutations of 1) 4-hand,  while Mr Boss has also looked at all 4-hands given a 5-hand.)

If, say, we require all 5-hands given a 4-hand,  I suggest it’s sufficient to solve for 
0 1 2 3.  All solutions for other 4-hands are equivalent after mapping.  

eg,  if we require the solution for h =. 3 5 8 13,  the to-vector is 
      to =. 3 5 8 13 0 1 2 4 6 7 9 10 11 12 14 .... 51,
ie h, h-.~ i.52

If the canonical solution for i.4 is S, the solution for 3 5 8 13 is 
     to { S .

I assume the order of the 4-hand is partially significant,  in that the first pair prescribes required cards, and the second pair excluded cards. If desired,  we could 
set, or perhaps require: 
   h =. (/:~ 2{.h),  /:~ _2{.h   .

The mapped solution, (to { S) , may,  if required,  be re-sorted within hands and between hands to exactly reproduce a solution generated by other mechanisms discussed in this thread. 

Apologies if this is so painfully obvious that it didn’t need stating.  Even more if it’s wrong!

Mike

Sent from my iPad