Mrs. Hudson’s Problem #2 - the solution
- Last Updated on Wednesday, 28 November 2012 18:00
- Written by Vitaly Novikov
Surely, this was a difficult question in our series of Sherlock Holmes Mahjong Mysteries. Yet, some readers solved it quite quick!
This was the situation:
Mrs. Hudson said that she would not collect even a Pair, not meld, not collect Flowers. “I hope that I would not discard a tile to somebody’s mahjong otherwise that would offend others”, she said.
Then, she drew the last tile from the wall. Then she asked Mr. Wan Tao, what tile she could safely discard in order to not give mahjong?
Mr. Tao looked looked at the hands iof all four players and said: “Mrs. Hudson, you can discard a safe tile due to the fact that all of your 14 single tiles would suit to somebody’s mahjong. Even more, despite there is no even a pair in your hand you have mahjong, so, please, declare it!”
So, the question was: reconstruct all four hands.
And the expert question was: provide a solution under the condition of a dead hand for Lestrade.
Answer. Mrs. Hudson’s hand (“Greater Honors and Knitted Tiles”):
Surely one of gentlemen’s hands (Mr. Holmes’s one) should be “Thirteen Orphans” wait (13 single Terminals or Honors) calling for the following 7 Honors and 2 Terminals out of Mrs. Hudson’s hand:
Now, two other hands have to wait for , , , and .
Two other hand are very simple “Pure-suiter-waits” with waiting tiles (plus a Pair) in “Craks” hand and (plus a Pair) in “Dots” hand.
Answer (for experts). Let’s start with the same Mrs. Hudson’s and Mr. Holmes’ hands.
Now, to cope with wait on sparse tiles in two suits like , , , , we need to utilize structure with co-called “chameleons” (see additional section below on “chameleons”). Dr. Watson’s hand is (hand is concealed):
Strictly speaking 8 pts. for mahjong the above hand is gaining after fan “Last Tile Claim”.
By definition, “chameleon” (term was first used in 2005 at my site http://www.mahjong-co.narod.ru/waits_analysis.html) is a structure with number of one-suited tiles = 3*X+2 (i.e., 2, 5, 8, 11) which form a legal regular mahjong structure in both occasions:
1. NO tiles added (“Chameleon sits straight”) – “X” groups by 3 tiles (normally, Chows) and a Pair,
2. 1 tile added (“Chameleon puts out its tongue”) – “X+1” groups by 3 tiles (normally, Chows) and a Pung.
In a case Dr. Watson’s hand,
may be split as:
1. + + -- no tiles added, or
2. + + when is added,
3. + + when is added,
4. + + when is added.
And may be split as:
1. + -- no tiles added, or
2. + when is added.
3. + when is added.
Dr. Watson’s hand consists of two chameleons each of them can “sit straight” (no tile added) or “put out its tongue” (a tile is added to form legal structure).