Holmes, Watson, Lestrade and Mrs. Hudson are playing mahjong game. Today's game is special because our foursome decided to determine the best player of the season. Whoever wins the game will be named as best player. In case of shared winners, a new game will be played.

Before the last deal, the score looked strange and funny: all three gentlemen have +18 points while Mrs. Hudson has -54 points. At this point time, all the gentleman are willing to win by any means.

Prizes generously provided by the publishers of Mahjong Collector Magazine, and by Holiday Mahjong Online.

At some points of time gentlemens' hands looked similar:

  • Holmes --  with one tile in his hand,
  • Watson --  with one tile in his hand,
  • Lestrade --  with one tile in his hand,
  • Mrs. Hudson has declared two chows so far.

In other words, all gentlemen have as the main fan of their hand a 16-points fan consisting of three pure chows shifted by step one, two or three. Everybody can be waiting for any tile since 18 points are already within the respective melded sets.

Since the lady is 72 points away, then the strategy of each gentlemen was, beside simply winning the game and the title of best player, to not not give mahjong to another gentlemen. It was Lestrade who chose to deal a "safe" discard directly into Mrs. Hudson's "Hu".

Question 1 (): Please, provide Mrs. Hudson's hand (both melded and concealed parts) under two conditions:

  • her hand has a 3-sided wait leading to a hand containing a 16-points fan, and consisting of three pure chows shifted strictly by step one for one waiting tile, by step two for the other waiting tile and by step three for the third waiting tile.
  • her winning hand contains a "Tile Hog" of .

Question 2 (): Who won the game?

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  • Guest - Denl

    Question1. Mrs. Hudson's hand is melded chows 678-789 of characters, concealed 2345688 of characters. She is waiting on 1,4,7 with result of:
    1: 123-456-678-789-88 pure shifted chows by step three;
    4: 234-456-678-789-88 pure shifted chows by step two;
    7: 234-567-678-789-88 pure shifted chows by step one.
    Question2. Mrs. Hudson won this game with result of 14 (or 15) points and two gentlemen had 10 points each and Lestrade had -34(or -35).
    Mrs. Hudson hand was 24+16+2+2(+1 in case of 4,7)=44 points (full flash, three pure shifted chows, all chows, tile hog (+short straight)).

  • Guest - marco montebelli

    1- melded part: 678 789 char.; concealed part: 2345688 char.. she's waiting for 1 (shift 3), 4 (shift 2), 7 (shift 1) char..
    2- in any case the winner is mrs. hudson: avoiding points of flower(s) or for possible last tile, she counts 42 points with 1 and 43 with 4 or 7. the final ranking become (at least): hud 12 (or 13), hol 10, wat 10, les -32 (or -33).

  • By 1:30 p.m. already 10 solutions have been received. It looks like not a difficult mystery at all!!

  • Guest - Sylvain MALBEC

    Considering the new description, here come my new answer:
    Mrs. Hudson's hand was:
    Melded: 678wan 789wan
    Concealed: 2345688wan
    (waiting on 1, 4, 7wan)

    She scores:
    Either Pure Shifted Chows or Pure Straight (16)
    Full Flush (24)
    Tile Hog (2)
    All Chows (2)
    Maybe Short Straight (0 or 1)
    Last Tile (4)
    -------------------
    Total: 48 or 49 points, the thrower (Lestrade) pays 72 or 73 points.

    If Lestrade has discarded the 1wan, he pays 72 points, and Mrs. Hudson, Holmes, Watson all tie for the first place.
    If Lestrade has discarded the 4 or 7wan, he pays 73 points, and Mrs. Hudson wins by one single point.

    Of course, she could also have "Last Tile Claim" and win in any case.
    Or not having "Last Tile", so only Holmes and Watson will be tied for first place.


    I'll say she won on 1wan, forcing the triple tie, for the sake of dramatic effect.

  • Guest - Sylvain MALBEC

    My bad -_-'

    Not counting Last Tile, the correct scoring is (without/with Short Straight):
    Holmes: 18 - 8 = +10
    Watson: 18 - 8 = +10
    Lestrade: 18 -8 - 44/45 = -34/-35
    Mrs. Hudson: -54 + 24 + 44/45 = +14/+15

    Mrs. Hudson wins in any case.

  • Mrs Hudson may have 678 and 789 of characters in her melded sets and 2345688 of characters in her concealed hand. This gives her a three-sided wait:

    • 1 gives her 123, 456, 678, 789, 88 => full flush (24), pure straight (16), last tile (4), all chows (2), tile hog (2) = 48.
    • 4 gives her 234, 456, 678, 789, 88 => full flush (24), pure shifted chows with step 2 (16), all chows (2), tile hog (2), short straight (1) = 45.
    • 7 gives her 234, 567, 678, 789, 88 => full flush (24), pure shifted chows with step 1 (16), last tile (4), all chows (2), tile hog (2), short straight (1) = 49.

    Lestrade did not discard 4, because that would have been a dangerous tile from his point of view: Hudson has one such tile in her concealed hand, but it could equally well have been Holmes or Watson! On the other hand, 1 and 7 may well have been safe if enough of each had been discarded previously. By the same logic, 1 and 7 give Hudson the Last Tile fan.

    Hudson may also have the Last Tile Claim fan (8), but we aren’t given enough information to determine this.

    After Mrs Hudson’s hu:
    • Holmes and Watson each pay Mrs Hudson 8 points, so they now have +10 points each.
    • Lestrade pays Mrs Hudson (48 or 49) + 8 points, so he now has −46 or −47 points.
    • Mrs Hudson receives a total of (48 or 49) + 24 points, so she now has +18 or +19 points.

    As this was the last deal, Mrs Hudson wins the game and the title.

  • Guest - Anh-Vu Tran

    Hello,

    Here is my answer for this new mystery. I had some trouble to find the hand of Mrs. Hudson, but after a lot of investigation, the only possible hand is:
    - melded chows 678 and 789
    - concealed hand 2345688
    All tiles are in character suit.
    - win on 1c discard: 123 456 789 678 88 - Full Flush + Pure Straight + Tile Hog + All Chows = 44 pts
    - win on 4c discard: 234 456 456 678 88 - Full Flush + Pure Shifted Chows + Tile Hog + All Chows + Short Straight = 45 pts
    - win on 7c discard: 567 678 789 234 88 - Full Flush + Pure Shifted Chows + Tile Hog + All Chows + Short Straight = 45 pts

    Mrs. Hudson will score 44 or 45 pts fans. In the scenario 44 pts, final scores are:
    - Mrs. Hudson has -54 + 44 + 24 = 14 points
    - Lestrade has 18 - 44 - 8 = -34 points
    - Holmes has 18 - 8 = 10 points
    - Watson has 18 - 8 = 10 points
    Therefore Mrs. Hudson wins the game. Obviously, she also wins the game if she gets the 45 points fans hand.

    Lestrade's discard was not so "safe". During the game, he didn't have enough time to think of Mrs. Hudson's actual hand ;-)

    All the best,
    Anh-Vu

  • Guest - Quentin

    Mrs. Hudson's hand was made of only Craks, more exactly 678 and 789 were melded Chows, while 2345688 was concealed. Hence Mrs. Hudson was ready on Craks 1, 4 and 7, that other players would rather consider as a "safer" tile.
    Hand scores at least Full Flush (24), All Chows (2) and Tile Hog (2) => 28 points.

    • Craks 1 => Pure Straight (16) => 44 points;
    • Craks 4 => 2 - Pure Shifted Chows + Short Straight (17) => 45 points;
    • Craks 7 => 2 - Pure Shifted Chows + Short Straight (17) => 45 points.

    After this hand Mrs Hudson wins the game whatever the winning tile: 72 point-difference is caught up by little by payment, even for Holmes and Watson [44+32=76].

  • Guest - Matthieu

    Hi Vitaly,
    Here is my answer:
    Melded
    678 789
    Concealed
    23456 88

    1 => 123 456 678 789 88
    4 => 234 456 678 789 88
    7 => 234 567 678 789 88

    Pure hand: 24 pts
    Pure shifted chows: 16 pts
    All chows: 2 pts
    Tile hog: 2 pts
    (Short straight: 1pt with 4 or 7)

    Total : 44pt or 45 pts

    Final result (considering 44pts)
    Lestrade: 18-(44+8) = -34
    Holmes & Watson: 18-8 = +10
    Mrs. Hudson: -54+(44+8*3) = +14

    Final result (considering 45pts)
    Lestrade: 18-(45+8) = -35
    Holmes & Watson: 18-8 = +10
    Mrs. Hudson: -54+(45+8*3) = +15

    Mrs. Hudson wins the game.

  • Guest - Menno Deij

    Hi Vitaly,

    I think I finally solved it - but for some reason it took me quite long...

    The open hand is 678 789
    The closed hand is 23456 88

    The wait is for 1-4-7
    1: 123-456-789-678-88 (straight: step 3)
    4: 234-456-678-789-88 (pure shifted 234-456-678: step 2)
    7: 234-567-678-789-88 (pure shifted 567-678-789: step 1)

    All have a tile hog in 8.

    Now for the score:

    1: full flush (24) pure straight (16) tile hog (2) all chows (2) => 44 points
    4: full flush (24) pure shifted (16) tile hog (2) all chows (2) short straight (1) => 45 points
    7: full flush (24) pure shifted (16) tile hog (2) all chows (2) => 44 points

    Whichever tile was thrown (1, 4 or 7) Mrs. Hudson wins.

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