Solution to the puzzle Sleuth

Sleuth is one of the puzzles of the Melbourne University Puzzle Hunt 2005 competition co-created by the founder of WikiLeaks, and likely organizer of the Cicada 3301 community, Julian Assange (the other author of the puzzle is Andrew Kwok). This is an interesting and original task. At the same time it is quite voluminous, and its peculiarity is a large amount of irrelevant information. 

According to the plot of the game, you find yourself inside a mysterious dark castle, where you become a witness of a strange conversation. 7 people take part in the discussion, and they all speak different languages. One of them is the host; he speaks english. The other 6 people are his guests; they speak Chinese, Dutch, French, German, Italian and Japanese. Apparently, a terrible crime has occurred in the castle, and the host suspects one of the guests. Together they try to unravel this case…

It's easy to see a reference to the board game Cluedo. This exciting game was invented in the middle of the twentieth century in the United Kingdom. Over time it became very successful and was published in many countries. The game is played by 3 to 6 people. The scene is a mansion owned by Mr. Black. The mansion has nine different rooms: the Hall, Lounge, Dining Room, Kitchen, Ballroom, Conservatory, Billiard Room, Library and Study. Some of these rooms are additionally interconnected by secret passages.

One evening Mr. Black is found murdered in his mansion. It is known, that in that day he met six guests, each of whom had a vivid biography. They were: Miss Scarlett, Colonel Mustard, Mrs. White (in modern editions her place is taken by Dr. Orchid), Reverend Green, Mrs. Peacock and Professor Plum. It is known, that one of the guests committed the murder, and one of six items could be the crime weapon: the candlestick, dagger, revolver, rope, lead pipe or wrench.

Now the participants of the game have to solve this difficult case. With the help of questions to the other players and logical reasoning, they need to answer 3 questions: who killed Dr. Black, in which room did it happen, and what served as a weapon…

However, if you take a look at the dialogue, it may seem that there are more than 6 names in it. At this point Puzzle Hunt participants were required to find a site on the internet, dedicated to the game Cluedo, or rather its section called International: «Have you ever wondered what Cluedo/Clue is like in other countries - well here are the answers...» In the section you can see what names the corresponding elements of the game have in editions on different languages. It consists of 3 tables: the first is dedicated to characters, the second to weapons, and the third to rooms. It turns out, that each participant in the conversation named the elements of the game in accordance with the Cluedo edition in their own language. I propose to go over this dialogue at the same time noting information, that will be useful in the future.

Host: “Ladies and gentlemen, if you'd kindly like to follow me along the corridor, through the hall to that room over there. It’s best that we all remain there after this shock. We must have this incident sorted out. In the mean time, I’ll have my servants search for it. I’m fairly sure it’s still somewhere in the castle.”

 
„Da?“ 
German: „There?“

- Pourquoi il nous est interdit de partir cette salle?

French: «Why are we forbidden to leave this room?»

「他の六つの部屋は立ち入り禁止にしなければなりません。午後 四時に起きた事件の証拠が残っている可能性がありますからね。 」 

Japanese: «The other six rooms should be closed, as they may contain evidence of an incident, that occurred at four o'clock in the afternoon.»

「我喜歡這間房。我相信這是這間堡壘的最舒適的房。我想我會坐 在白太太和藍夫人隔鄰。」 
Chinese: «I like this room. I believe it's the most comfortable room in the fort. I think I'll sit next to Mrs. White and Mrs. Peacock.»
(The Chinese is not Mrs. White [白太太] or Mrs. Peacock [藍夫人].)

“Wel, laten vij dan het doen.” 
Dutch: “Well, let's do it then.”

«Da quanto tempo impiegerà?» 
Italian: «How long will it take?»

Host: “It all depends on you, of course. Seeing that it took place over such a short period of time, we shouldn’t be too long. Still, I don’t understand why one of you was so desperate to take it. Did any of you notice anything suspicious since the alarm went off?” 

- Alors, j'ai remarqué un chandelier sur le plancher de la salle à manger comme nous marchions ici.

French: «So, I noticed a candlestick on the dining room floor, as we were walking here.»
(The candlestick [chandelier] was in the Dining room [salle à manger].)

«Signiora Bianchi sembra essere molto sospettata. L'ho vista andare fuori dalla biblioteca sembrava nervosa.» 

Italian: «Mrs. White seems to be highly suspected. I saw her go out of the library, she looked nervous.»
(Mrs. White [Signiora Bianchi] was in the Library [biblioteca]. The Italian is not Mrs. White.)

「昼食の時、プラム教授のポケットからロープがはみ出ている のに気づきました。そういえば、そろそろ夕食の時間ですね。 シェフは厨房でオードブルの準備をしているのか。」 

Japanese: «During lunch, I noticed a rope sticking out of Professor Plum's pocket. Come to think of it, it's almost dinner time. Is the chef in the kitchen preparing hors d'oeuvres?»
(Professor Plum [プラム教授] had the rope [ロープ]. The Japanese is not Professor Plum.)

Host: “Ōdoburu? Ah yes, should be ready soon.” 

- J’ai soif. Est-ce qu’il y a quelqu’un qui voudrait aussi un verre de vin? Il y a trois personnes qui en voudraient – Le Colonel Moutarde, Mademoiselle Rose et moi. Alors, peut-être que je demanderai au cuisinier d’apporter deux bouteilles de vin. 

French: «I am thirsty. Would anyone like a glass of wine too? There are three people, who would like it – Colonel Mustard, Miss Scarlett and me. So maybe I'll ask the cook to bring two bottles of wine.»
(The French is not Colonel Mustard [Le Colonel Moutarde] or Miss Scarlett [Mademoiselle Rose].)

“Wel, ik gelouf dat ik Mw. Blaauw van Draet in de biljartkamer zag toun ik door degang loopt.” 

Dutch: “Well, I believe I saw Mrs. Peacock in the billiard room, when I walk down the hall.”

(Mrs. Peacock [Mw. Blaauw van Draet] was in the Billiard room [biljartkamer]. The Dutch is not Mrs. Peacock.)

„Meiner Meinung nach scheint Fräulein Gloria, als ob sie seit heute Morgen sehr böse ist. Nach Mittagessen sah ich ihr. Sie klammerte einen Dolch um.“ 

German: „It seems to me, that Miss Scarlett has been very angry since this morning. After lunch I saw her. She was clutching a dagger.“

(Miss Scarlett [Fräulein Gloria] had the dagger [Dolch]. The German is not Miss Scarlett.)

Host: “Ah, we seem to have collected quite a bit of information. It really is terrible to have to go through all this, but as it seems all of you had the means to do it, I have no other choice. Would anyone like to add anything?” 

„Ich habe Baronin Von Porz beobachtet, als ich dieser Abend vorbei an ihr im Korridor gegangen bin. Sie hielt einen Leuchter. Sie müssen zugeben, dass das sehr ungewöhnlich ist.“ 

German: „I observed Mrs. Peacock, as I passed her in the corridor this evening. She held a candlestick. You have to admit, that this is very unusual.“ 

(Mrs. Peacock [Baronin Von Porz] had the candlestick [Leuchter]. The German is not Mrs. Peacock.) 

- Alors, je pense que j'ai vu Le Révérend Olive partant du bureau. Il s’en fallait de beaucoup qu’il soit heureux.

French: «So, I think I saw Reverend Green leaving the study. He was far from being happy.»
(Reverend Green [Le Révérend Olive] was in the Study [bureau]. The French is not Reverend Green.)

«Beh, adesso mi ricordo. Penso che abbia visto una chiave inglese per terra in qualque stanza. Mi ricordo che sigillavano la stanza. Ma dov’era? Ma sì, è giusto. Non penso che nessuno abbia menzionato questa stanza fin adesso.» 

Italian: «Well, now I remember. I think I saw a wrench on the floor in some room. I remember them sealing the room. But where was it? But yeah, that's right. I don't think anyone has mentioned this room yet.»
(The wrench [chiave inglese] was seen in one of the rooms.)

「溫室? 」 

Chinese: «Conservatory?»
(Perhaps in the Conservatory [溫室]?)

«Sì, è quella.» 

Italian: «Yes, that's it.»
(So, the wrench was in the Conservatory.)

“Na lunchen, zag ik Mw. de Wit en engelse sleutel dragen. Zij heeft gezegt dad zij ites moest opknappen.” 

Dutch: “After lunch I saw Mrs. White carrying the wrench. She said, she had to fix things up.”

(Mrs. White [Mw. de Wit] had the wrench [engelse sleutel]. The Dutch is not Mrs. White.)

「たしか書斎の中で、百科事典のとなりにピストルを見た覚えが あります。」 

Japanese: «I remember seeing a revolver in the library next to the encyclopedia.»
(The revolver [ピストル] was in the Library [書斎].)

「我相信我見到綠先生藏了一條鉛管在他的上衣。還有, 當一切都完了後, 是否有人有興趣和我打一場麻將? 」 

Chinese: «I believe I saw Reverend Green hide a lead pipe in his jacket. Also, would anyone be interested in playing a game of Mahjong with me when it's all over?»
(Reverend Green [綠先生] had a lead pipe [鉛管]. The Chinese is not Reverend Green).

Host: “Májiàng? Yes! That sounds like a wonderful idea. I was thinking the same thing. However given the number of people, you’ll probably have to pair up. Any suggestions for your preferred partner?” 

“Dominee Groenewoud of Kolonel van Geelen.” 

Dutch: “Reverend Green or Colonel Mustard.”

(The Dutch is not Reverend Green [Dominee Groenewoud] or Colonel Mustard [Kolonel van Geelen].)

- Madame Leblanc. C’est un excellent joueur.

French: «Mrs. White. She's an excellent player.»
(The French is not Mrs. White [Madame Leblanc].)

«Il Colonnello Mustard, Miss Scarlett o Il Reverendo Green.» 

Italian: «Colonel Mustard, Miss Scarlett or Reverend Green.»
(The Italian is not Colonel Mustard [Il Colonnello Mustard], or Miss Scarlett [Miss Scarlett], or Reverend Green [Il Reverendo Green].)

「わかりません。ただ、前回麻雀をした時に、ピーコック夫人 とスカーレット嬢が泣かされました。トリプル役満とは滅多に 出ないからねぇ・・・」

Japanese: «I don't know. But the last time we played Mahjong, Mrs. Peacock and Miss Scarlett made me cry. It's rare to see a triple yakuman...»
(The Japanese is not Mrs. Peacock  [ピーコック夫人] or Miss Scarlett [スカーレット嬢].) 

„Professor Bloom oder Oberst von Gatow.“ 

German: „Professor Plum or Colonel Mustard.“

(The German is not Professor Plum [Professor Bloom] or Colonel Mustard [Oberst von Gatow].) 

Host: “Excellent. It looks like we’re all in agreement. In fact, if nothing had happened, I had hoped we would start this afternoon. But now, we really must sort this out first. I have all the information I need.”

-Vraiment? 

French: «Really?»

Host: “Nevertheless, I am disappointed. It seems that one of you has been lying about the finer details of what happened this afternoon.” 

「私達の間にそのような行いをする者はいるはずがない。」 

Japanese: «None of us should act like this.»

Host: “What I am more disappointed in, however, is that the rest of you have failed to mention this detail. Why is that? Could it be that there’s something the rest of you are unwilling to reveal?” 

“Wat bedoeld je?” 

Dutch: “What do you mean?”

- Je ne sais pas à quoi m’en tenir. Que c’est étrange!

French: «I don't know what to expect. How odd!»

„Die Person wollte jeder natürlich verwirren.“ 

German: „The person wanted to confuse everyone, of course.“

«Chi è?» 

Italian: «Who is?»

Host: “You’ll soon out soon enough. Even though the rest of you did not provide the full details of what the culprit did, I still know what happened. In fact, I know exactly what happened to the very last detail amongst the six of you.” 

「啊, 真的嗎? 」 

Chinese: «Ah, really?»

Host: “Yes. I ask the culprit to come forward. Confess what you did. Tell us the exact details, in your own words, especially the one I alluded to earlier. Perhaps I might be lenient. That is all I have to say.” 

All the information that we noted can be divided into two parts. One part is the relationships between the characters and their nationalities. The other part is the relationships between the elements of the game, namely characters, weapons, and rooms. It makes sense to bring together all the available information for each group. Let's start with the nationalities of the characters.

• The Chinese is not Mrs. White, or Mrs. Peacock, or Reverend Green.
• The Dutch is not Mrs. Peacock, or Mrs. White, or Reverend Green, or Colonel Mustard.
• The French is not Colonel Mustard, or Miss Scarlett, or Reverend Green, or Mrs. White.
• The German is not Miss Scarlett, or Mrs. Peacock, or Professor Plum, or Colonel Mustard.
• The Italian is not Mrs. White, or Colonel Mustard, or Miss Scarlett, or Reverend Green.
• The Japanese is not Professor Plum, or Mrs. Peacock, or Miss Scarlett.

You can rewrite this information as follows.

• The Chinese is either Miss Scarlett, or Colonel Mustard, or Professor Plum.
• The Dutch is either Miss Scarlett, or Professor Plum.
• The French is either Professor Plum, or Mrs. Peacock.
• The German is either Mrs. White, or Reverend Green.
• The Italian is either Professor Plum, or Mrs. Peacock.
• The Japanese is either Reverend Green, or Colonel Mustard, or Mrs. White.

If you pay attention to the French and the Italian, it is obvious that one of them is Professor Plum, and the other is Mrs. Peacock. Therefore, the other participants in the dialogue cannot be these characters. In this case the Dutch is Miss Scarlett, and the Chinese is Colonel Mustard. For the German and the Japanese Mrs. White and Reverend Green are remain.

• The Dutch is Miss Scarlett.
• The Chinese is Colonel Mustard.
• The French and the Italian are Professor Plum or Mrs. Peacock.
• The Japanese and the German are Reverend Green or Mrs. White.

Next, let's put together all the information about the elements of the game.

• According to the French, the candlestick was in the Dining room.
• According to the Italian, Mrs. White was in the Library.
• According to the Japanese, Professor Plum had the rope.
• According to the Dutch (Miss Scarlett), Mrs. Peacock was in the Billiard room.
• According to the German, Miss Scarlett had the dagger.
• According to the German, Mrs. Peacock had the candlestick.
• According to the French, Reverend Green was in the Study.
• According to the Italian, the wrench was in the Conservatory.
• According to the Dutch (Miss Scarlett), Mrs. White had the wrench.
• According to the Japanese, the revolver was in the Library.
• According to the Chinese (Colonel Mustard), Reverend Green had the lead pipe.

You can pick the information in respect of which there is a single opinion.

• According to the French and the Chinese (Colonel Mustard), Reverend Green was in the Study with the lead pipe.
• According to the Japanese, Professor Plum had the rope.
• According to the German, Miss Scarlett had the dagger.

However, further reports diverge. According to the German and the French, Mrs. Peacock was supposed to be in the Dining room with the candlestick. But according to the Dutch (Miss Scarlett), Mrs. Peacock was in the Billiard room. According to the Italian and the Japanese, Mrs. White was in the Library with the revolver. On the other hand, if we take the reports of the Dutch (Miss Scarlett) and the Italian together, Mrs. White must have been in the Conservatory with the wrench. As the host noted, one of the guests lied to the others. In both inconsistencies, there is an evidence from Miss Scarlett. Obviously, she was a liar and the person, who «wanted to confuse everyone». Therefore, she committed the crime. Thus, the following information is reliable.

• Reverend Green was in the Study with the lead pipe.
• Mrs. Peacock was in the Dining room with the candlestick.
• Mrs. White was in the Library with the revolver.
• Professor Plum had the rope.
• Miss Scarlett had the dagger.
• The wrench was in the Conservatory.

The reports of Miss Scarlett are unreliable.

• Mrs. Peacock was in the Billiard room.
• Mrs. White had the wrench.

If we played Cluedo and we were sure, that Miss Scarlett had committed the murder with the dagger, then now, in order to win, it remained to name the room. It was the detail about which, according to the host, the culprit lied and the other guests did not report. This is the Billiard room. The host wanted to hear about this detail from the culprit «in your own words». So, Miss Scarlett was required to come forward and name the room in her own language, in keeping with the rest of the dialogue. In the Dutch version of the game the Billiard room is called Biljartkamer. This word was the answer to the puzzle.