Problem Statement

There is a highly organized city that has decided to assign a number to each of their departments:

Each department can have a number between   1   and   7   (inclusive). The three department numbers are to be unique (different from each other) and must add up to   12. The Chief of the Police doesn't like odd numbers and wants to have an even number for his department.

Write a computer program which outputs all valid combinations.

Possible output   (for the 1st and 14th solutions):

Let's start with the solution:

function main {
  set -- Police Sanitation Fire
  typeset -i pw=${#1} sw=${#2} fw=${#3}
  printf '%s' "$1"
  shift
  printf '\t%s' "$@"
  printf '\n'
  for (( p=2; p<8; p+=2 )); do
    for (( s=1; s<8; ++s )); do
      if (( s == p )); then
        continue
      fi
      (( f = 12 - p - s ))
      if (( f == s || f == p || f < 1 || f > 7 )); then
        continue
      fi
      printf "%${pw}d\t%${sw}d\t%${fw}d\n" "$p" "$s" "$f"
    done
  done
}

main "$@"