I was just using Roger's problem statement. If you want to make it independent of index origin, replace <: with (- >./@,)
http://mathworld.wolfram.com/LatinSquare.html says a Latin square uses numbers 1-n. FWIW. Henry Rich On 10/4/2010 8:57 PM, Don Guinn wrote: > I made a simple Latin square and tried your definition. > > z=:3 3$1 2 3 2 3 1 3 1 2 > z > 1 2 3 > 2 3 1 > 3 1 2 > hr=:-.@(0&e.)@:(C.!.2)@(,|:)@:<:"2 > hr z > 1 > hr>:z > 0 > > I think that incrementing all numbers in z should still produce a Latin > square. > > > > > > > On Mon, Oct 4, 2010 at 7:13 PM, Henry Rich<[email protected]> wrote: > >> I got to >> >> -.@(0&e.)@:(C.!.2)@(,|:)@:<:"2 >> >> as the test for whether the item is a Latin square. I have been trying >> to find some cool test, without success. >> >> Henry Rich >> >> On 10/4/2010 7:37 PM, Roger Hui wrote: >>> Great minds think alike, eh? (But I think you >>> need to test your expressions ;-) Go to >>> http://www.jsoftware.com/jwiki/Essays/KenKen >>> and look about a third of the way down, >>> >>> q #~ (8$15) -:"1 (+/"1 ,. +/"2) q{0,2^i.4 >>> >>> The initial effort in your previous msg is also >>> similar to my initial effort. >>> >>> >>> >>> ----- Original Message ----- >>> From: Marshall Lochbaum<[email protected]> >>> Date: Monday, October 4, 2010 16:28 >>> Subject: Re: [Jprogramming] Distinct Numbers in Rows and Columns >>> To: 'Programming forum'<[email protected]> >>> >>>> Here's a funny--and much faster--one: >>>> p=.p:i.n >>>> *./"1 (*/p) = (*/"2 ,. */"1) q{p >>>> >>>> Actually, I suppose it is better to do it with addition, so >>>> p=.2^i.n >>>> *./"1 (+/p) = (+/"2 ,. +/"1) q{p >>>> >>>> Marshall >>>> >>>> -----Original Message----- >>>> From: [email protected] >>>> [mailto:[email protected]] On Behalf Of Roger Hui >>>> Sent: Monday, October 04, 2010 6:41 PM >>>> To: Programming forum >>>> Subject: [Jprogramming] Distinct Numbers in Rows and Columns >>>> >>>> An interesting puzzle arising from the KenKen solver: >>>> q is an array with shape (m,n,n) and (,q) e. 1+i.n . >>>> Which items of q have 1+i.n in each row and in each column? >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
