The Dueling Pistols by Ilya Repin (1899) at the State Historical Museum, Moscow

Current mystery starts story of opposition of Sherlock Holmes and Professor Moriarty at the latest London MCR Championship. Key deals and techniques will be highligted and discussed.

Before the last deal of the first session Moriarty leads 80 game points. The deals starts but with only three minutes left until the end of the session. Moriarty (East) picks up an impossible starting hand: . Other days it is perfect to try even "Nine Gates" but this time the only priority is to finish the hand safely in three minutes. He discards . After South's move West discards some Dot tile (Moriarty cannot pung it) and Holmes (North) declares Chow discarding . Professor takes  and after discarding Bamboo the hand has already a 3-sided wait: for  and . Once again after South moves West discards another Dot tile (not for Moriarty's wait), Holmes declares Chow discarding . One minute has left to the end of session.

Now, an incredible thing has happened: the wind blows open the windows and overturns five of Holmes' tiles exposing  with only two tiles left unexposed. Moriarty takes . He understands that no matter how the exposed tiles are to be treated -- intentionally or unintentionally exposed -- he has to make a discard. Despite this, he has the option to throw as many as nine different tiles, yet all nine of those tiles could be dangerous to discard and possibly costly should he deal in to a mahjong in Sherlock's hand. Whenever there is a space for a guess, even a mastermind can guess wrong. Moriarty discards a tile.

"Hu," declares Holmes. "Pure Shifted Chows -- 16 points, Half Flush -- 6 points, Seat Wind -- 2 points, Prevalent Wind -- 2 points. 16+6+2+2=26 points in total."

Holmes has won the session with only 2 point lead.

Note: Moriarty could observe two exposed Chows in Holmes hand. For instance, for  and  dangerous discards potentially giving 16-points fan would be  or  (yielding "link"-Chow  for completing high-scoring fan). Moriarty lost because two Chows made potentially dangerous to discard all nine tiles in Moriarty's hand.

Question (): Please, provide two melded Chows of Sherlock's hand which made potentially dangerous to discard all nine tiles in Moriarty's hand. In other words, any of tiles  or  can be used in Chow which creates with two exposed Chows 16-points fan "Pure Shifted Chows".

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Comments (11)

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  • Guest - Jinbi Jin

    Note that there are at most three ways in which two Chows of the same suit can be completed to a Pure Shifted Chows; one with a Chow "to the left", one with a Chow "to the right", and one with a Chow "in the middle". In other words, the two Chows should fit as the two Chows in the center in a Four Shifted Chows pattern with shift 2, so the only possible Chows are 345 and 567, making Chows 123, 789, and 456 dangerous. In fact, Moriarty can see only three of each dots tile, so every dot tile is indeed potentially dangerous.

  • Guest - Sylvain MALBEC

    Holmes' melded chows are 345 and 567dot.
    It could form:
    123-345-567 (dangerous: 123)
    345-456-567 (dangerous: 456)
    345-567-789 (dangerous: 789)

  • Guest - Marco montebelli

    Three- four- five and five -six -seven

  • Guest - Marco montebelli

    3-4-5 and 5-6-7

  • Guest - Menno Deij

    Good morning Vitaly,

    The two melded chows are 345 and 567

    with 1, 2 or 3 this completes to 123-345-567 (having 23, 13 or 12 as wait respectively)
    with 4, 5 or 6 this completes to 345-456-567 (having 56, 46 or 45 as wait respectively)
    with 7, 8 or 9 this completes to 345-567-789 (having 89, 79 or 78 as wait respectively)

    Best wishes,

    Menno Deij - van Rijswijk

  • Guest - Cyrille

    Let's suppose the two melded chows exposed by Holmes are 345 and 567. This is possible if West discards twice a 5 dots for example.
    Holmes can complete "Pure Shifted Chows" either with 123, 456 or 789. In each case the value of the hand will be at least 26 points, meaning a difference of 84 points (26*2+32) with Moriarty on this game. So there is no safe tile for Moriarty.

  • Guest - Anh-Vu Tran


    If 9 dot is dangerous, it means that Holmes needs a chow 789d to win. This leaves two options for Pure Shifted Chows :
    - 345 567 melded + 789
    - 567 678 melded + 789
    Moreover, Holmes didn't count Edge Wait or Closed Wait and I assume he is a good player, he didn't miss any fan. Therefore he wins on 9d discard.
    Thus Moriarty keeps two 7d in his hand.
    Since the one tile spaced version of Pure Shifted Chows requires three 7d, this is not possible.
    Finally Holmes has melded chows 345d and 567d. He has 78d + three Nord Winds + two Red Dragons. He wins on 9d discard.

    Wasn't that elementary ?

  • Holmes may have 345 567 as his exposed chows:

    • 1 may be needed for 123 (345 567).
    • 2 may be needed for 123 (345 567).
    • 3 may be needed for 123 (345 567).
    • 4 may be needed for (345) 456 (567).
    • 5 may be needed for (345) 456 (567).
    • 6 may be needed for (345) 456 (567).
    • 7 may be needed for (345 567) 789.
    • 8 may be needed for (345 567) 789.
    • 9 may be needed for (345 567) 789.

    Holmes may have initially had 34 67 in his hand and called chow on 5 both times. Neither 5 was useful to Moriarty in any way. In total, Moriarty’s and Holmes’ hands contain at most four 1s (3+1), at most two 2s (1+1), at most three 3s (1+2), at most three 4s (2+2), at most four 5s (1+3), at most two 6s (1+2), at most four 7s (2+2), at most two 8s (1+1) and at most four 9s (3+1), so there are enough tiles for this to be possible.

  • As many as 10 correct answers have been received during the first day for this easy mahjong mystery.

  • Guest - Quentin

    Melded Chows were 345 and 567. PSC is completed with either 123, 456 or 789 of the same suit, making all tiles of that suit dangerous.

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