[Guest]

Clue is a rather popular board game that requires deduction and reasoning

For my questions these are the rules to follow:

There are always 6 people playing at the start of the game, you are one of those 6.

There are 6 suspects

Mustard

Scarlet

White

Plum

Green

Peacock

There are 6 weapons

Wrench

Rope

Candlestick

Knife

Pipe

Pistol

There are 9 rooms

Kitchen

Dining Room

Lounge

Hall

Study

Library

Observatory

Spa

Patio

There are cards representing each suspect, weapon, and room

At the start 1 suspect, 1 weapon, and 1 room will be randomly chosen and placed in an envelope

At the start each player recieves 3 random cards, they are not any of the 3 placed in the envelope and they can be any combination of suspects, weapons, and rooms.

Ex. You could get 3 room cards, or you could get 2 suspects and a weapon, etc.

As each person takes his/her turn they will make a guess, of the suspect, weapon, and room.

They will always make exactly one guess each turn.

Then if one of the other 5 people can disprove either of the 3 things guessed they will show the guesser and only the guesser one of the 3 cards guessed.

These are my questions:

1. What are the best 3 cards to get to have the best odds of guessing the 3 cards in the envelope without anyone taking any turns?

2. Is it possible to KNOW the 3 cards in the envelope in one turn (each person guesses once), assume the best case scenario. If not in the best case what is the minimum number of turns required before you KNOW the 3 cards in the envelope?

3. What are the worst 3 cards to start with?

4. Assume the worst case, what is the maximum number of turns that can be taken before you KNOW the contents of the envelope?

5. What are the odds that someone will KNOW the contents of the envelope before YOU KNOW the contents of the envelope?

[bonanova]

Either three suspect cards or three weapons cards.

In either case there are 162 possible solutions.

Three room cards.

Now there are 216 possible solutions.

All hands:

Three persons [or weapons] - 162 cases

Two persons and one weapon [or v.v.] - 180 cases

Two persons [or weapons] and one room - 192 cases

One person, one weapon and one room - 200 cases

One person [or weapon] and two rooms - 210 cases

Three rooms - 216 cases

For question 5 is it assumed that you are the first player?

[Gmaster479]

Clue is easily my favorite board game.

When people guess in clue, everyone has to try to disprove a guess when someone makes it. So if you are the first player and you enter a room and guess 3 random cards that you don't currently have in your hand and no one disproves you or shows you another card, then you know those are the cards in the envelope.

If you weren't that lucky, then you would have to get one room, and then 2 suspects and 3 weapons (or 3 suspects and 2 weapons). Then everyone would have to enter the same room (with each suspect being moved to that room when you guess them) you have in your hand, and the person there guesses one of your suspects OR weapons and someone else shows them a card. Do this 5 times so that each time the only card that is possibly shown to the guesser is the one you don't have. On the 6th turn (lets say you are Plum), you would have to go in a different room, and then guess the weapon and suspect you know it is (or just one's from your hand) and hope that you got lucky and entered the correct turn. Either way it can be done in one turn, whether it be by 100% luck or 90% deduction and 10% luck

Assume you have 0 rooms. Now assume that when every player guesses that isn't you, that you can't deduce a single card that was played. Then you would have to make sure you avoid the rooms that you have cards for and take a guess each time. You need to see 5 suspects, 5 weapons, and 5 rooms at the most. Then it would be 15 turns until you knew assuming one guess per turn. Now lets be mean and say you get a one every turn and start from Mr. Green's spot (the worst on the board), assuming you are smart enough to aim for all the rooms as fast as possible, it could take you as many as 35 turns if you avoid the room you have. Next to that, you can only do worse if you don't play the game correctly.

[Guest]

Yes, for question 5 you do go first, sorry I forget to say that

@gmaster479 in this problem I'm not meaning for you to have to move to make a guess, if I wasn't clear what i was trying to say was that everyone will ALWAYS make 1 guess every single turn and the room for that guess can be any room they want, they don't need to be in the room they guess

and yeah I see what your saying with question 2, you could always have a chance of knowing your first turn, so i'm going to change it to this.

2. Assuming the best case scenario is it possible to KNOW the contents of the envelope in 1 turn, IF every guess is proved wrong (by someone showing them a card), if not what is the minimum number of turns that need to be taken to KNOW the contents of the envelope.

Edited July 12, 2009 by K4D

[Guest]

This game very interesting, but there are efforts to think, my God, thinking of my weaknesses

[Guest]

I think I've got an answer for 2 (revised):

I'm not sure if this is the spirit of your question exactly, but it can be solved by Player 1 after only three guesses (not even a full round). This assumes that a couple of the items in the envelope are guessed immediately.

My Scenario:

Envelope contains:

Green

Pipe

Patio

P1 has:

Wrench

Rope

Candlestick

P1 guesses:

Green

Pistol

Patio

P6 shows: Pistol

From here we know that only P6 could have Green or Patio since everyone else passed.

P2 guesses:

Green

Rope

Patio

P1 shows: Rope

Now we know that Green and Patio must be in the envelope since P6 passed.

P3 guesses:

Green

Knife

Patio

P4 (or anyone) shows: (has to be) Knife

At this point, P1 has enough information to know that the Envelope contains: Green, Pipe, Patio

Again, I'm not sure if this is the sort of scenario you are asking about. If everyone always guesses 100% wrong answers, then I don't think that it could be solved in one round, but I'm not sure how many it would take.

[Guest]

Yes dawh that is what I was looking for, nice job

[Gmaster479]

Yes, for question 5 you do go first, sorry I forget to say that

@gmaster479 in this problem I'm not meaning for you to have to move to make a guess, if I wasn't clear what i was trying to say was that everyone will ALWAYS make 1 guess every single turn and the room for that guess can be any room they want, they don't need to be in the room they guess

and yeah I see what your saying with question 2, you could always have a chance of knowing your first turn, so i'm going to change it to this.

2. Assuming the best case scenario is it possible to KNOW the contents of the envelope in 1 turn, IF every guess is proved wrong (by someone showing them a card), if not what is the minimum number of turns that need to be taken to KNOW the contents of the envelope.

Alright, I got you. Good Job dawh. I love clue