NB. packages in the sleigh http://adventofcode.com/day/24

p=: \:~".(LF,' ')charsub CR-.~1!:1{:ARGV

comb=: 4 : 0 NB. http://www.jsoftware.com/jwiki/Essays/Combinations
 k=. i.>:d=.y-x
 z=. (d$<i.0 0),<i.1 0
 for. i.x do. z=. k ,.&.> ,&.>/\. >:&.> z end.
 ; z
)

test=: 4 : 0 NB. x - number of groups
  w=. +/y   NB. total weight
  t=. <.w%x NB. target weight of each group
  assert w=t*x NB. i.e. w is divisible by 3
  n=.>:+/t>+/\y NB. min number of items in a group
  m=.<.x%~#y    NB. max number of items in a group - 1/x-th of all
  for_k. n+i.>:m-n do.
    c=. k comb #y NB. n..m comb #y
    s=. c#~t=+/"1 c{y NB. it would be good to check if other parts are ok...
    if. 0<#s do. <./*/"1 s{y return. end.         NB. but some other time :)
  end. 0
)

echo 3 test p NB. 10723906903 - works good with downsorted, bad otherwise
echo 4 test p NB. 74850409

exit 0