"Watson," Holmes remarked, puffing on his pipe, “Isn’t that the paragraph about placing the winning tile into the hand?"

"Quite right," confirmed Dr. Watson. “And here is a quote of that rule":

"1.9. Clearly show your winning tile, either claimed or self drawn. Failing to do so results in not being allowed to claim points for 'Single, Edge or Middle wait', 'Last tile' and 'Nine Gates'."

Question

Please, explain how Mrs. Hudson was able to convince a judge to allow points on two separate occasions; once for two different fans as listed in rule 1.9, despite her having absent-mindedly violated the rule in question.

Scoring guidelines: each of two fans explained would bring 1 SHP (). 

Answer

The basic idea of the solution is despite the fact that Mrs. Hudson had placed the winning tile into her hand (technically negating the possibility of obtaining points for the fan in question), in her situation, the judge allowed the fan because it wouldn't have mattered which tile was her winning tile since ANY of the fourteen tiles in the concealed portion of her hand could meet the necessary condition of the fan under consideration.

This approach may look controversial and doubtful if you follow the letter of the "Regulations", however, the judge ruled in favor of Mrs. Hudson. So, what might these two fans be?

It is obvious that fans like “Closed Wait” and “Edge Wait” are not the case because among the three tiles of the chow there is at least one tile which would never meet criteria for the 1 point wait.

Also "Nine Gates" fan can not considered because it contains nine different suit tiles, eight of which could not meet criteria for that fan.

So, in the first appeal Mrs. Hudson had four pungs opened, and a tile was taken from the wall to make a pair and declare “Hu!”. Despite the fact that she did not clearly show which tile she picked, she was able to convince the judge that there is no difference which of the two identical tiles she put into her hand, so the fan was counted.

In the second appeal Mrs. Hudson announced mahjong on a knitted hand (“Greater/ Lesser Honors and Knitted Tiles”), putting the winning tile into her hand. During the scoring procedure she attempted to score points for the fan "Last Tile".

Fan #58 (worth 4 points) Last Tile: Winning on a tile that is the last of its kind. (It must be clear to all players based on the discards and exposures.)

 

Her opponents argued that she cannot do that because it is impossible to determine which tile to apply the fan "Last Tile" to.

Unbelievably, it turns out that for any of the 14 tiles in Mrs. Hudson’s hand, there were three copies of that same tile on the table amongst discards and melded sets! The judge again ruled in favor of Mrs. Hudson, since it wouldn't matter which of her fourteen tiles was the last, since all of them were the last of its kind.

Appendix: Here is an example how the hand may have worked out for the second appeal:

Mrs. Hudson is sitting as North, and her starting hand was almost a finished knitted hand (12 tiles are ready):

.

East discards  -- a useful tile to complete Mrs. Hudson’s hand. South and West in turn discard the same tile.

Mrs. Hudson takes  into her hand and then after discarding  she becomes waiting!

Suddenly, a "pangonada" occurs -- a cannonade of declared pungs broke out:

  • East declares “Pung!” and discards ,
  • South declares “Pung!” and discards ,
  • West declares “Pung!” and discards ,
  • East declares “Pung!” and discards ,
  • South declares “Pung!” and discards ,
  • West declares “Pung!” and discards ,
  • East declares “Pung!” and discards ,
  • South declares “Pung!” and discards ,
  • West declares “Pung!” and discards ,
  • South declares “Pung!” and discards ,
  • West declares “Pung!” and discards ,
  • East declares “Pung!” and discards ,
  • South discards ,
  • West discards .

Mrs. Hudson draws the 4th  from the wall, places it into her hand and then declares “Hu!”

In fact, out of the fourteen different tiles in Mrs. Hudson’s hand, one can find twelve examples where there are three copies of those tiles in form of melded pungs, and two examples where there are three copies of those tiles in the discard pool.