For example, if I define

parts=: (] #~ (%~ [EMAIL PROTECTED]) = +/"[EMAIL PROTECTED]) [: #:@i. 2&^&.<:
pieces=: [ ([EMAIL PROTECTED]@[ */ ]) parts

then believe that I can identify which members
of the outer product of the result of pieces I want
by forming an outer product and selecting only
those combinations which do not collide

valid=: (0 = [: +/"1 *"1//)@pieces

Unfortunately, I am drawing a blank on how to
find that outer product for the general case.
However, for some specific cases, +"1// seems
to work

Example:
   3 (valid #&(,/) +"1//@pieces) 6

Unfortunately, I do not have enough time right
now to think through where I went wrong.

-- 
Raul
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