# At a small economics conference, a photographer wants to line up nine 
# participants for a photo. Two of them — Robert and Milton — insist on 
# standing next to each other. How many different arrangements (lineups) 
# are possible?

keep = []
rest = []

perms = 123456789.to_s.chars.to_a.permutation.map(&:join)

for i in perms
  if i.to_s =~ /12/ then keep.push(i.to_s); next; end
  if i.to_s =~ /21/ then keep.push(i.to_s); next; end
  rest.push(i.to_s)
end

puts "keep.size == #{keep.size}"
puts "rest.size == #{rest.size}"
puts "perms.size== #{perms.size}"

# Output (first line is the answer):
# keep.size == 80640
# rest.size == 282240
# perms.size== 362880