Our foursome gathered to play mahjong at Baker Street 221 B. The wall is built and broken, tiles are dealt. And then Dr. Watson says:
"According to newspaper "Mahjong News" rules of mahjong game vary in different countries. For instance, what an amazing rule called the "Charleston" is in American mahjong. The essence of it is that before the game players pass three unwanted tiles to some other player and do that several times."
"Why all this?" asked Mrs. Hudson.
"It's easy!" said Holmes. "You give out unwanted tiles but may received good one exactly to collect mahjong."
"Provided that all tiles will fit to the place," said Inspector Lestrade.
"Why we do not try this rule, so as an experiment?" asked Mrs. Hudson. "For instance, I do not have in my hand any ready three-tile set (Chow or Pung). I would be eager to exchange three unwanted tiles for more suitable ones."
"Strange to say, I also do not have any ready three-tile set in my hand," replied Watson.
"And me! And me!" shouted Holmes and Lestrade.
"Well, well, it is decided!" said Mrs. Hudson sitting at East position. "Gentlemen, please, take three unwanted tiles and pass them to the player to your right. Let's see what happens".
Next moment something unexpected happened. Mrs. Hudson after receiving three different Honor tiles has in hand complete mahjong, while three gentlemen's hands become waiting for mahjong.
Question: Please, provide all four hands under conditions:
- hands before passing of tiles do not have any ready three-tile sets (Chow or Pung),
- group of passed tiles consisted strictly of three Bamboo, three Characters, three Dots, three different Honor tiles,
- there are no Flowers in hands,
- : main (maximum of points) fan for all four hands is strictly the same,
- : main (maximum of points) fan for all four hands is strictly different, sum of points of main fans of all four hands is maximal.
Note: Waiting hands for determining main fan are considered to be completed by adding appropriate waiting tile.