In the morning, Sherlock Holmes and Dr. Watson are sitting at the table waiting for Mrs. Hudson to bring them their morning coffee. "Mrs. Hudson is definitely delayed," said Watson. "I will go into the kitchen to see what's the matter."

It turnes out that Hudson is sitting at the table turning tiles back and forth and writing something.

"Mrs. Hudson, what are you doing? We are tired of waiting for our morning coffee!"

After bringing morning coffee, Mrs. Hudson explains:

"I'm trying to determine the maximum value of the mahjong hand for all valid types of structures."

"Well, the maximum value for the hand with a regular structure is known, which is 328 points without flowers, if I am not mistaken. For the hand with Big Three Dragons, All Honors etc.," said Watson.

"As written in the "Green Book" there are three more valid hand structure which are not regular:

  • "Seven Pairs"
  • "Thirteen Orphans"
  • "Lesser/Greater Honors and Knitted Tiles"

said Mrs. Hudson.

"I would also add here one more type -- "Semi-Regular" -- for the hand consisting of three knitted sequences of "Knitted Straight", Chow / Pung / Kong and a Pair," Holmes joined the conversation. "It is easy to distinguish types of hand structures. A regular hand has four times Chow / Pung / Kong and a Pair. This hand is allowed to declare sets, thus I would say it is also allowed to collect the hand  pieces. Three types of irregular hands consisting only of pairs and single tiles do not allow any declarations prior to "Hu". Finally, a Semi-Regular type of hand which allows only one declaration of a set." 

"So, Mrs. Hudson, what's your question?" asked Watson.

"Quite simple, to determine the maximum value of a hand for each hand structure. We speak here specifically about hand value, and not about total points won," said Hudson.

"Part of the issue, definitely, is investigation which fans or combinations of fans related to the winning tiles are applicable," continued Holmes. "Here is a list of those fans":

  • fan #44 Last Tile Draw,
  • fan #45 Last Tile Claim,
  • fan #46 Out with Replacement Tile,
  • fan #47 Robbing The Kong,
  • fan #56 Fully Concealed Hand,
  • fan #58 Last Tile,
  • fan #77 Edge Wait,
  • fan #78 Closed Wait,
  • fan #79 Single Wait,
  • fan #80 Self-Drawn.

 

Question: For each of the following four types of hand structure, please, determine the maximum value for the hand (without Flowers):

  • "Seven Pairs"
  • "Thirteen Orphans"
  • "Lesser/Greater Honors and Knitted Tiles"
  • "Semi-Regular" (three knitted sequences of "Knitted Straight", Chow / Pung / Kong and a Pair)

Note: Correct answers for one or two hand structures will be scored as , three or four as .

 

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