I can follow Henry's clever solution. 0 ": 6 %~ (-: 999998 * 999999) + 3 * -: 999998
83333333333 I tried to replicate Roger's partition approach, and ran into memory issues. Roger must have more memory on his machine: pnk 4 : 0"0 n=. 0>.x [ k=. y if. 1>:n<.k do. x: (0<n)*1=k else. ((n-1) pnk k-1) + (n-k) pnk k end. ) 1e2 pnk 3 833 1e3 pnk 3 83333 1e4 pnk 3 |stack error: pnk | ((n-1)pnk k-1)+(n-k) pnk k However, as Roger points out, this still does show the trend that the answer is likely 83333333333. Then I tried to replicate Roger's second approach: +/ <.@(%&2)@<: n - 3*i.<.n-3 [ n=: 1e2 _2207 +/ <.@(%&2)@<: n - 3*i.<.n-3 [ n=: 1e3 _247007 +/ <.@(%&2)@<: n - 3*i.<.n-3 [ n=: 1e4 _24970007 Engine: j807 /j64/windows Beta-c: commercial/2018-03-13T17:40:01 Library: 8.07.09 Qt IDE: 1.7.1/5.9.4 Platform: Win 64 Something's wrong here, as I can't replicate Roger's results, but I'm not sure what is going wrong. Skip On Sun, May 20, 2018 at 9:31 AM Henry Rich <henryhr...@gmail.com> wrote: > Taking advantage of the fact that thepartitions have only 3 elements. > > If the first number is i, the second number can be anything from 1 to > 999999-iand the third number is then uniquely fixed. > > Since ican run from 1 to 999998, the total number of such choices is (-: > 999998 * 999999). > > But this counts triplets more than once. Any triplet in which the > numbers are unique will be counted 6 times. > > Any triplet containing a repetition will be counted 3 times: once when i > is the unrepeated number and twice when i is the repeated number. This > happens here whenever i is even, thus > (-:999998) times. > > Any triplet containing all 3 numbers equal will be counted just once, > but there aren't any of them. > > To find the unique triplets, we take (-: 999998 * 999999), add in 3 * > (-:999998) to bring the 3-times-repeated cases up to 6-times-repeated, > then divide by 6: > > 0 ": 6 %~ (-: 999998 * 999999) + 3 * -: 999998 > > 83333333333 > > > Henry Rich > > > > --- > This email has been checked for viruses by AVG. > http://www.avg.com > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
