Questions

Question 1: What is the minimal number of tiles in the discards zone from a player who declared mahjong, provided that there are no tiles in the discard zones of any other player?

Question 2: What is the maximal number of tiles in the discard zone from a player who declared mahjong, provided that there are no tiles in the discard zones of any other player?

Question 3: What is the maximal number of tiles in the discard zone of all players, provided that number of discarded tiles for three of the players are equal, and there are no tiles in the discard zone of the 4th player?

Question 4: What is the maximal number of tiles in the discard zone from a player, provided that there are no tiles in the discard zones of the other players?

Question 5: What is the maximal total number of tiles in the discard zone from all the players, provided that there are no tiles in the discard zones of just some of players?

Scoring guidelines: correct answers to 2 or 3 questions brings 1 SHP (), to 4 or 5 questions brings 2 SHP (), not counting `early submission' bonus.

Answers

Comments: In the solution below:

  • “DZ” stands for “discard zone”,
  • “DZ=N” means that DZ has exactly N tiles,
  • “EDZ”, “SDZ”, “WDZ”, “NDZ” stand for discard zone of players: East, South, West, North.

General consideration: Please, note that:

  • regular hand structure “3+3+3+3+2” (where “3” may be Chow/ Pung/ Kong) allows claiming discards for sets/ mahjong declarations up to 5 times,
  • hand structure “3+2+3*Knitted Chows” allows claiming discards for set/ mahjong declarations only twice,
  • hand structures “7*2”, “14*1”, “2+12*1” are considered to be concealed, so they allow to claim discard only once, for mahjong.

Answer 1: 0. Obviously, mahjong was declared by East immediately after the phase of flower replacement.

Answer 2: 5. East starts deal and makes discard, EDZ=1. Further discards of South, West or North are intercepted by East, EDZ=2. The situation is repeated three more times until EDZ=5. Please, note, that any discard might be intercepted by Chow/ Pung/ Kong declaration of South, West or North at any stage. It is important that none of discards of South, West or North is left unclaimed.

Answer 3: 15 (three times 5 tiles). Mahjong will be declared by North. East (the player to the right of the North) starts discarding, EDZ=1. This is followed by South, SDZ=1, and West, WDZ=1. North’s discard is taken by East, so NDZ=0, and East has one melded set. Another round of discards leads to EDZ=SDZ=WDZ=2. North’s discard is taken again by East, so NDZ=0, and East has two melded sets. Let’s repeat procedure two more times. EDZ=SDZ=WDZ=4, NDZ=0, East has four melded sets. Now, another round of discards leads to EDZ=SDZ=WDZ=5. North declares mahjong from the wall, so NDZ=0. Please, note that some of discards of North or even East may be taken by South or West, though it is crucial that East ultimately has to intercept last discard of that series.

Answer 4: 5. Getting tile in DZ after discard interception is possible only when declaring set/ mahjong. 4 melded sets of a player means DZ=4 for that player. Additional tile in DZ is only possible after discarding in the first move, so the player is East. The solution coincides with Answer 2.

Answer 5: 27! Mahjong will be declared by North. The solution partly resembles Answer 3, though there is no need for the number of tiles in EDZ, SDZ and WDZ to be equal. So, after WDZ=5 (as in Answer 3 solution) North’s discard is taken by South (!), since 4 sets of East have already been melded, EDZ=5. South discards, one set of South is melded, SDZ=6, West discards, WDZ=6. Repeating procedure three more times we have: EDZ=5, SDZ=9, WDZ=9, only West has concealed hand. Now, North’s discard is taken by West (!), and repeating procedure three more times after West’s discard we come to EDZ=5, SDZ=9, WDZ=13, totaling 5+9+13=27 tiles in DZ while NDZ=0. North, in turn, declares mahjong from the wall.