How Many Solutions Exist in Clue (Cluedo)? The Math Behind the Mystery

The classic deduction game Clue (Cluedo) has exactly 324 possible case solutions.

The Math

Each solution combines one suspect, one weapon, and one room:

• 6 Suspects: Miss Scarlett, Colonel Mustard, Mrs. White, Mr. Green, Mrs. Peacock, Professor Plum.
• 6 Weapons: Candlestick, Dagger, Lead Pipe, Revolver, Rope, Wrench.
• 9 Rooms: Hall, Lounge, Dining Room, Kitchen, Ballroom, Conservatory, Billiard Room, Library, Study.

6 × 6 × 9 = 324 unique combinations.

Gameplay Implication

At game start, one random combination is placed in the envelope. The remaining 18 cards are dealt to players. Through suggestions and deductions, players eliminate possibilities until only the envelope's trio remains.

Variants Note

• Clue Master Detective (1988): 10 suspects, 8 weapons, 12 rooms → 960 solutions.
• Themed editions (Harry Potter, Rick and Morty, etc.) usually keep 6/6/9 but rename elements.
• Two-player rules add a "ghost hand" but don't change solution space.

324 is the canonical number for standard Clue — enough for high replayability, few enough for human deduction.