CLUEDO PUZZLE from The Actuary magazine You are the Actuary; you have Miss Scarlett, Revolver and Ballroom in your hand. There is no board; the players simply take turns to make suggestions. PLAYER CHARACTER WEAPON ROOM DISPROVED BY ------------------------------------------------------------------------------ Banker Col. Mustard Dagger Billiard Room Economist Cleric Prof. Plum Lead Piping Study Economist Doctor Mrs White Spanner Conservatory Farmer Economist Rev. Green Spanner Library Farmer Farmer Mrs Peacock Revolver Hall Actuary Actuary Rev. Green Candlestick Dining Room Farmer (Dining Room) Banker Mrs Peacock Rope Ballroom Economist Cleric Col. Mustard Spanner Lounge Banker Doctor Prof. Plum Dagger Kitchen Banker Economist Prof. Plum Lead Piping Study Banker Farmer Mrs White Lead Piping Conservatory Economist It is your turn. Who committed the murder, with what weapon, and where? SOLUTION -------- STARTING OFF ------------ There are six suspects, six weapons and nine rooms. One of each is in the murder cards envelope, which leaves 18 cards dealt among six players, so three cards each. The Economist has disproved four suggestions. He has: Colonel Mustard, or the Dagger, or the Billiard Room, and Professor Plum, or the Lead Piping, or the Study, and Mrs White, or the Lead Piping, or the Conservatory, and Mrs Peacock, or the Rope, or the Ballroom. We know he hasn't got the Ballroom because we've got it. So he's got Peacock or Rope, and two other cards from the first three disprovings. Therefore he must have the Lead Piping; if he didn't, then to disprove the first three suggestions he disproved he'd have to have four cards, which he doesn't. So we know the Economist has the Lead Piping. The Banker disproved the Economist's suggestion of Plum, Piping, Study, and the Economist has the Piping, so therefore the Banker must have Plum or Study. ORDER OF SUGGESTION ANSWERING ----------------------------- When you make a suggestion, the player to your left must answer it first. If they cannot disprove your suggestion, the player to their left may do so, and so on in strict order. When the Doctor suggested White, Spanner, Conservatory, the Economist would have been first to get the opportunity to disprove the suggestion, and he could not. So the Farmer disproved it. We now know the Economist doesn't have any of those cards. So now the Economist has: Mustard OR Dagger OR Billiard Room, AND Plum OR Piping OR Study, AND Piping, AND Peacock OR Rope. Therefore he has (Peacock or Rope), (Lead Piping) and (Mustard or Dagger or Billiard Room). He can't have Plum or Study because that means he'd also have to have Mustard, Dagger or Billiard Room, and that would be four cards in total. The Banker suggested Mustard, Dagger, Billiard Room, and neither the Cleric nor the Doctor had any of those. From the next suggestion (Cleric suggested Plum, Piping, Study, disproved by Economist) we also know the Doctor doesn't have Plum, Piping or Study. When the Actuary suggested Green, Candlestick, Dining Room, nobody except the Farmer had any of those cards - he showed Dining Room. The Banker suggested Peacock, Rope, Ballroom, and the Cleric and Doctor had none of these. The Cleric suggested Mustard, Spanner, Lounge, and nobody but the Banker had any of these. The Doctor suggested Plum, Dagger, Kitchen, and the Economist and Farmer had none of those. This means the Economist doesn't have Mustard or Dagger. From our earlier deduction about his hand, he therefore has Billiard Room, Lead Piping, and Peacock/Rope. The Farmer has Dining Room, White/Conservatory and Green/Library. We can eliminate Billiard Room, and we've already eliminated Lead Piping. Finally, the Farmer suggested White, Piping, Conservatory, and nobody but the Economist had any of these cards. ONCE YOU HAVE ELIMINATED THE IMPOSSIBLE... ------------------------------------------ By elimination, the Doctor can only have three cards: Library, Hall and Kitchen. All other cards are either known to be held by someone else, or part of a suggestion which he had the opportunity to disprove but could not. So none of these cards can be in the secret envelope. Also, the fact that the Doctor has the Library must mean the Farmer, who as shown above has Green/Library, must have Rev Green. We can eliminate him. The Cleric has three of Plum, Spanner, Study, Hall, Library, Lounge, Kitchen, again by elimination from all the facts above. Since we know three of those cards are in the Doctor's possession, that leaves Plum, Spanner, Study, Lounge. Let's go back to the Banker. We know he has Mustard/Spanner/Lounge, and Plum/Study, and Plum/Dagger. We also know that the Cleric has three of Plum, Spanner, Study and Lounge, so the Banker can only have a maximum of one of those four cards. Suppose the Cleric has Plum, Spanner, Lounge: the Banker would have Mustard, Study, Dagger. Suppose the Cleric has Plum, Study, Lounge: this is impossible, as we know the Banker has Plum or Study. Suppose the Cleric has Plum, Spanner, Study: this is impossible for the same reason. Suppose the Cleric has Spanner, Study, Lounge: the Banker would have Mustard, Plum and possibly Dagger. So the Banker either has Mustard, Study, Dagger, or Mustard, Plum and another card. Either way he's got the Colonel, so eliminate him. Also the Cleric has Plum, Spanner, Lounge, or Spanner, Study, Lounge. Either way he's got the Spanner and the Lounge. THE ENDGAME ----------- At this point, the hands are as follows: Actuary: Scarlett, Revolver, Ballroom. Banker: Mustard, Plum/Study, Plum/Dagger. Cleric: Spanner, Lounge, Plum/Study. Doctor: Library, Hall, Kitchen. Economist: Billiard Room, Lead Piping, Peacock/Rope. Farmer: Dining Room, Green, White/Conservatory. Suspects not eliminated: Plum, White, Peacock. Weapons not eliminated: Dagger, Candlestick, Rope. Rooms not eliminated: Study, Conservatory. The Cleric has got Plum or Study, so therefore the Banker doesn't have Plum and Study. So he's got Mustard, Plum, Dagger, or Mustard, Study, Dagger. Either way he's got the Dagger, so Dagger's eliminated. This means the Banker's got Mustard, Dagger, Plum/Study, and the Cleric's got Spanner, Lounge, Plum/Study. We don't know which of them has Plum and which of them has Study, but we don't much care. We can eliminate both Plum and Study from our enquiries. Suspects not eliminated: White, Peacock. Weapons not eliminated: Candlestick, Rope. Rooms not eliminated: Conservatory. We now know the murder was committed in the Conservatory. We also know that the Farmer has got Dining Room, Green, White/Conservatory. This becomes Dining Room, Green, White, which also eliminates White and means Mrs Peacock must be the murderer. J'ACCUSE -------- The Economist has Peacock or Rope, and he hasn't got Peacock. So he's got the Rope, which eliminates the Rope and means the murderer was Mrs Peacock, with the Candlestick, in the Conservatory.