GroupMaker Pro™ (all props to @gfredericks)

group_maker.rb

require 'set'
names = [
  # student names here
]

def get_group_set(coll)
  if coll.count % 4 == 0
    coll.each_slice(4).to_a
  else
    [coll[0..2]] + get_group_set(coll[3..-1])
  end
end

def get_random_group_set(students)
  get_group_set(students.shuffle).map(&:to_set)
end

def compatible_group_sets?(p1, p2)
  (p1 & p2).count <= 2
end

def find_groups(students, max_tries, max_groups=10)
  return [] if students.count < 6
  group_sets = [get_random_group_set(students)]
  tries = 0
  while tries < max_tries
    break if group_sets.count > max_groups
    new_group_set = get_random_group_set(students)
    if group_sets.all? {|p| compatible_group_sets?(p, new_group_set) }
      group_sets << new_group_set
      tries = 0
    else
      tries += 1
    end
  end
  group_sets
end

groups = find_groups(names, 2, 5)
groups.map do |x|
  puts x.each_with_index.map {|y,i| "#{i+1}: #{y.to_a.join(', ')}" }
  puts
end
puts "There were no groups found for these students." if groups.empty?