Where do you get the requirement that the numbers must be unique? The problem stated here was:
"How many distinct triplets have a sum of 1,000,000 (provided all numbers are integers and are positive)?" The quora statement of the issue is slightly different, but substantially the same: "How many distinct unordered triplets of positive integers have a sum of 1,000,000?" No occurrences of "unique integers" anywhere that I can see... just a requirement that each triplet be considered unique (and that the order of the integers within a triplet is irrelevant). Thanks, -- Raul On Sun, May 20, 2018 at 7:59 PM, Don Guinn <dongu...@gmail.com> wrote: > Yes, I had a bug in my previous definition for triplescount. Stupid. Should > have checked more before speaking. > > But As I understand the problem, the numbers in each triple should be > unique. Looking at has several triples with duplicate numbers. > > t #~ 3=#&>t > +-----+-----+-----+-----+-----+-----+-----+-----+ > |8 1 1|7 2 1|6 3 1|6 2 2|5 4 1|5 3 2|4 4 2|4 3 3| > +-----+-----+-----+-----+-----+-----+-----+-----+ > > The values (8 1 1; 6 2 2; 4 4 2; 4 3 3) are not unique leaving > 7 2 1; 6 3 1;5 4 1;5 3 2 > +-----+-----+-----+-----+ > |7 2 1|6 3 1|5 4 1|5 3 2| > +-----+-----+-----+-----+ > > which is what I get in the triples definition below. Same except the order > in each row is reversed. > > triples 10 > 1 2 7 > 1 3 6 > 1 4 5 > 2 3 5 > > I rewrote triplescount and made a triples as follows. This time I followed > my logic in my previous e-mail which I didn't in the definition of > triplescount then: > > triples=:3 : 0 > n1max=.<:<.y%3 > n1=.>:i.n1max > n2max=.<:>.-:y-n1 > n2=.n1+&.>(<@:>:@i.)"0 n2max-n1 > n1n2=.;(<"0 n1),.&.>n2 > n1n2,.y-+/"1 n1n2 > ) > > triplescount=:3 : 0 > n1max=.<:<.y%3 > n1=.>:i.n1max > n2max=.<:>.-:y-n1 > +/n2max-n1 > ) > > triples &.>6+i.10 > +-----+-----+-----+-----+-----+-----+-----+------+------+------+ > |1 2 3|1 2 4|1 2 5|1 2 6|1 2 7|1 2 8|1 2 9|1 2 10|1 2 11|1 2 12| > | | |1 3 4|1 3 5|1 3 6|1 3 7|1 3 8|1 3 9|1 3 10|1 3 11| > | | | |2 3 4|1 4 5|1 4 6|1 4 7|1 4 8|1 4 9|1 4 10| > | | | | |2 3 5|2 3 6|1 5 6|1 5 7|1 5 8|1 5 9| > | | | | | |2 4 5|2 3 7|2 3 8|1 6 7|1 6 8| > | | | | | | |2 4 6|2 4 7|2 3 9|2 3 10| > | | | | | | |3 4 5|2 5 6|2 4 8|2 4 9| > | | | | | | | |3 4 6|2 5 7|2 5 8| > | | | | | | | | |3 4 7|2 6 7| > | | | | | | | | |3 5 6|3 4 8| > | | | | | | | | | |3 5 7| > | | | | | | | | | |4 5 6| > +-----+-----+-----+-----+-----+-----+-----+------+------+------+ > triplescount &>6+i.10 > 1 1 2 3 4 5 7 8 10 12 > (#@:triples) &>6+i.10 > 1 1 2 3 4 5 7 8 10 12 > > The results above look right. Please correct me if I'm wrong. > > Below tried several triplescount's and see a pattern, but a little > different from what others are getting. > > triplescount"0] 10^>:i.7x > 4 784 82834 8328334 833283334 83332833334 8333328333334 > > Well, this has been fun. > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
