# Introducing The NEW AND IMPROVED Mystery X Game

Gold Member

## Main Question or Discussion Point

- The game proceeds by rounds. At the start of each round, X is some mystery individual. A round begins by the latest winner (or me for the first round) attributing one property to X. Ex:
or
X is in my car.
or
X is a dead president of the USA.
- A property must apply to more than one individual. An individual is not a property. Ex:
X is a suspension bridge that opened in 1937 and spans the Golden Gate.
and
X is the first president of the USA
are not allowed because they only apply to one individual: The Golden Gate Bridge and George Washington, respecitvely.
- Each property added must narrow the current possible candidates for X. Ex:
to the list of properties
X is a president of the USA.
X was born before 1800.
is not allowed because it doesn't narrow the possibilities (all presidents of the USA born before 1800 are dead).
- Some X having all of the properties listed must actually exist (be it real or fictional). Figments of your imagination do not count- you can't just make things up.
- A round ends when the list of properties applies to only one individual, or no one has added another property to the list for 2 hours. The last person to add a property to the list is the winner. Ex.
Round 1
Dick: X was a president of the USA.
Harry: X was born in 1732. This ends the round- the list of properties applies to one individual: George Washington.
Round 2
Harry: X is red.
Dick: X was opened in 1937.
Harry: X is a suspension bridge in California.
etc.
- So that's it- you just keep building a list of properties until the list applies to one individual. That should cover it. I think it could get interesting if you choose the properties wisely. I'll start.

X is a prime number less than 5.

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Moonbear
Staff Emeritus
Gold Member
:uhh: This still doesn't quite work. AKG's suggestion in the first version might fix the problem. He suggested you LOSE if you are forced to give a property that only applies to one individual rather than that making you the winner, otherwise we could all win just by jumping to the narrowest property. So, in your round 1 example, Harry loses and Dick wins (because he was the last person to give a property applying to more than one individual). If we reach the time limit before getting that narrow, the last person to give a property within the time limit wins that round.

So, who's keeping score?

X is a prime number less than 4.

(This first one is probably not a really good one to play with since there's not much room for creativity; let's just do this one as a sample round to work out the rules and then we'll start the real thing.)

Gold Member
Moonbear said:
:uhh: This still doesn't quite work. AKG's suggestion in the first version might fix the problem. He suggested you LOSE if you are forced to give a property that only applies to one individual rather than that making you the winner, otherwise we could all win just by jumping to the narrowest property. So, in your round 1 example, Harry loses and Dick wins (because he was the last person to give a property applying to more than one individual). If we reach the time limit before getting that narrow, the last person to give a property within the time limit wins that round.

So, who's keeping score?

X is a prime number less than 4.

(This first one is probably not a really good one to play with since there's not much room for creativity; let's just do this one as a sample round to work out the rules and then we'll start the real thing.)
Okay, gimme a sec to read AKG's post. We don't need to keep score. You can if you want to.

X is a prime number less than 4. doesn't narrow the possibilities (which are 2 and 3, both less than 4).

Gold Member
Moonbear said:
He suggested you LOSE if you are forced to give a property that only applies to one individual rather than that making you the winner, otherwise we could all win just by jumping to the narrowest property.
That's why I have the rule that you cannot add a property that applies to only one individual.
So, in your round 1 example, Harry loses and Dick wins (because he was the last person to give a property applying to more than one individual).
But Dick didn't force Harry to pick George Washington. Harry allowed Dick to choose George Washington by narrowing the options enough. Of course, you can force someone to win, just like I'm making the next person win by excluding 2 or 3. People can also jump in and add properties to foil someone who seems to have a plan. And we don't take turns, so anyone can jump in and win. Just give it a chance. If it doesn't work my way, we can switch to AKG's.

X is a prime number less than 6 (giving 2, 3, 5).

Then you still could have won with:

X is less than 3.

Because "less than 3" applies to more than one individual. But when combined with the other property in the list, it applies to a single individual: 2.
Plus, you aren't confined to math- math can be easy, but real world categories are ripe with complicated sets of properties.

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AKG
Homework Helper
There's a technical flaw in your game. Suppose the first person says "x is in A." The second person can give the property "x is a OR x is b" where a is in A, b is in B, and A and B are disjoint. This second property does not apply to an individual, since it applies to two distinct things. However, the conjunction of both properties clearly applies only to one individual, a. This is why I mentioned in the previous thread that it might be difficult to place appropriate restrictions to make this game work, unless you're extremely creative. We could actually make a game out of this. You (or some people) try to continually add rules that make the game work and still be fun, while others continually try to find loopholes that ensure that the second person wins.

Gold Member
AKG said:
There's a technical flaw in your game. Suppose the first person says "x is in A." The second person can give the property "x is a OR x is b" where a is in A, b is in B, and A and B are disjoint. This second property does not apply to an individual, since it applies to two distinct things. However, the conjunction of both properties clearly applies only to one individual, a.
Bah, why do people want to sabotage my game? That is very sneaky, but if b is not in A, then "x is in A and x is b" is false, and I already have a rule that says some X with the properties must exist. When P is false, P v Q <=> Q, so "x is a OR x is b" is equivalent to "x is a". If "x is a" applies to only one individual, it isn't allowed because I already have a rule you cannot add a property that applies to only one individual.
:grumpy:
This is why I mentioned in the previous thread that it might be difficult to place appropriate restrictions to make this game work, unless you're extremely creative. We could actually make a game out of this. You (or some people) try to continually add rules that make the game work and still be fun, while others continually try to find loopholes that ensure that the second person wins.
Fine, let's hurry up and fix it so I can start playing.

AKG
Homework Helper
honestrosewater said:
Bah, why do people want to sabotage my game? That is very sneaky, but if b is not in A, then "x is in A and x is b" is false, and I already have a rule that says some X with the properties must exist. When P is false, P v Q <=> Q, so "x is a OR x is b" is equivalent to "x is a". If "x is a" applies to only one individual, it isn't allowed because I already have a rule you cannot add a property that applies to only one individual.
Then your game is impossible. My initial complaint was going to be that you had two contradictory rules:

- A property must apply to more than one individual.
- A round ends when the list of properties applies to only one individual

But then I realized that it is possible for no single property to only apply to an individual while the entire list does. You have to look at each property as a standalone property, and check whether it applies to at least one individual. Then you have to check whether the set of things that satisfies all properties contains only one member. Nonetheless, I still found a flaw and that was the subject of my previous post. Your response would, however, incur the objection above (the one I was initially going to make but never did). If you're taking all previously listed properties into account to determine whether a new one restricts the list to only one thing, then one can win the game if and only if he adds an illegal property.

Moonbear
Staff Emeritus
Gold Member
honestrosewater said:
That's why I have the rule that you cannot add a property that applies to only one individual.
But that's exactly what the winner has to do, give a property that only applies to one individual. That's the part that has me most confused.

But Dick didn't force Harry to pick George Washington. Harry allowed Dick to choose George Washington by narrowing the options enough. Of course, you can force someone to win, just like I'm making the next person win by excluding 2 or 3. People can also jump in and add properties to foil someone who seems to have a plan.
So let's say you started as you did with
X is a prime number less than 5.
This leaves us with 1, 2 or 3, right?
So, what stops me from jumping directly to:
X is greater than 2?
See, if that meant I'd lose, then I wouldn't do that, I'd prefer to say,
X is greater than 1. That would narrow the choices down by one more, but not leave a single answer left, which means I'm forcing the next person into the losing spot (or else nobody takes that guess and I still win due to the time-out rule).

I guess what I'm trying to get at is, let's say we started with something more general, like X is blue. I could then narrow it down to X is found in North America, which is still pretty broad and leaves lots of different choices, or I could jump right to X is a type of berry, which pretty much leaves one answer. Every round could end in just two clues if there isn't some restrictions or some reason to avoid ending a round.

And we don't take turns, so anyone can jump in and win. Just give it a chance.
Okay, okay, okay, we can give it a chance. Don't cry!
How about I start one and then I can't complain that I don't know what to do next. :tongue2:

X is found above ground.

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wolram
Gold Member
Moonbear said:
But that's exactly what the winner has to do, give a property that only applies to one individual. That's the part that has me most confused.

So let's say you started as you did with
X is a prime number less than 5.
This leaves us with 1, 2 or 3, right?
So, what stops me from jumping directly to:
X is greater than 2?
See, if that meant I'd lose, then I wouldn't do that, I'd prefer to say,
X is greater than 1. That would narrow the choices down by one more, but not leave a single answer left, which means I'm forcing the next person into the losing spot (or else nobody takes that guess and I still win due to the time-out rule).

I guess what I'm trying to get at is, let's say we started with something more general, like X is blue. I could then narrow it down to X is found in North America, which is still pretty broad and leaves lots of different choices, or I could jump right to X is a type of berry, which pretty much leaves one answer. Every round could end in just two clues if there isn't some restrictions or some reason to avoid ending a round.

Okay, okay, okay, we can give it a chance. Don't cry!
How about I start one and then I can't complain that I don't know what to do next. :tongue2:

X is found above ground.
I think that HRWWB has come up with a good one, lets give it a go, i can not
stand any weepies, want a tissue rose?

x is not on the ground

AKG
Homework Helper
X is either the International Space Station or AllTel Stadium (in or around Jacksonville, Fla. I would imagine). I win ;)

Gold Member
AKG said:
Then your game is impossible. My initial complaint was going to be that you had two contradictory rules:

- A property must apply to more than one individual.
- A round ends when the list of properties applies to only one individual

But then I realized that it is possible for no single property to only apply to an individual while the entire list does. You have to look at each property as a standalone property, and check whether it applies to at least one individual. Then you have to check whether the set of things that satisfies all properties contains only one member. Nonetheless, I still found a flaw and that was the subject of my previous post. Your response would, however, incur the objection above (the one I was initially going to make but never did). If you're taking all previously listed properties into account to determine whether a new one restricts the list to only one thing, then one can win the game if and only if he adds an illegal property.
Well, I don't know second order logic- and it's GD- so please be a pal and cut me some slack :) Pix is a term in the ordered list implies
$$\exists x \exists y (P_{i}x \wedge P_{i}y \wedge x \not= y)$$ (applies to more than one individual)
$$\exists x (P_{1}x \wedge ... \wedge P_{n}x)$$ (exists)
$$\exists x (P_{1}x \wedge ... \wedge P_{i}x \wedge \neg P_{i+1}x)$$ (narrows)
Actually, I can't defend my original "solution" to your loophole and can't think of a non-ad hoc way around it just now.

Gold Member
Moonbear said:
So let's say you started as you did with
X is a prime number less than 5.
This leaves us with 1, 2 or 3, right?
1 is usually not prime (depends on your definition, of course). I intended 1 not to be prime. So you are left with 2 and 3. You must exclude one of them, and in doing so, you narrow it down to one individual, so you win :) Even if I had said "X is a prime number less than 9999999999", you could still win by adding "X is less than 3" or "X is even" or "X is a factor of 13", etc. The first challenge is to think of something that can't be narrowed down to a single individual on the next turn.
So, what stops me from jumping directly to:
X is greater than 2?
See, if that meant I'd lose, then I wouldn't do that, I'd prefer to say,
X is greater than 1. That would narrow the choices down by one more, but not leave a single answer left, which means I'm forcing the next person into the losing spot (or else nobody takes that guess and I still win due to the time-out rule).
That's AKG's version. In my version, the person who narrows it down to one individual wins.
I guess what I'm trying to get at is, let's say we started with something more general, like X is blue. I could then narrow it down to X is found in North America, which is still pretty broad and leaves lots of different choices, or I could jump right to X is a type of berry, which pretty much leaves one answer. Every round could end in just two clues if there isn't some restrictions or some reason to avoid ending a round.
So the first person who posted "X is blue" should have thought ahead and realized that you could win by adding "x is a berry" (let's say), so they shouldn't have chosen to start with "X is blue". They're loss- you just won.

Gold Member
wolram said:
I think that HRWWB has come up with a good one, lets give it a go, i can not
stand any weepies, want a tissue rose?
Aw, thank you. You're such a nice guy.

Gold Member
We can still have fun until the loopholes are fixed.

X is found above the ground.
X is not on the ground.
X has an F in its name.

x is not a mammal

Gold Member
X has exactly 3 'F's in its name.

Gold Member
Okay, I'm leaving soon. If no one adds another clue, I was thinking:

X is the F-16 Fighting Falcon.

X is found above the ground.
X is not on the ground.
X has an F in its name.
X is not a mammal.
X has exactly 3 'F's in its name.

Farmers Feeding Families is an X with exactly 3 'F's in its name. And the new one:

X fought in a war.

honestrosewater said:
Okay, I'm leaving soon. If no one adds another clue, I was thinking:

X is the F-16 Fighting Falcon.

X is found above the ground.
X is not on the ground.
X has an F in its name.
X is not a mammal.
X has exactly 3 'F's in its name.

Farmers Feeding Families is an X with exactly 3 'F's in its name. And the new one:

X fought in a war.
Wouldn't Farmers Feeding Families lack the "X is not on the ground" property?

Gold Member
TheStatutoryApe said:
Wouldn't Farmers Feeding Families lack the "X is not on the ground" property?
AAAAAAAAAAHHHHHHHHHH! :rofl: :rofl: :grumpy: :uhh: :tongue2:

Okay, the rule is that every property that you add must by itself apply to more than one individual. That is, separately each property in the list must separately apply to more than one individual separately separately. :tongue2: That is, ignoring everything else in the list, each property, on its own, applies to more than one individual.

X is found above the ground. (Yes, this applies to more than one individual.)

X is not on the ground. (Yes, this applies to more than one individual.)

X has an F in its name. (Yes, this applies to more than one individual.)

X is not a mammal. (Yes, this applies to more than one individual.)

X has exactly 3 'F's in its name. (Yes, this applies to more than one individual: F-16 Fighting Falcon, Farmers Feeding Families, etc.)

The point of the rule is to prevent people from just naming an individual in one turn.

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Gold Member
ANd, BTW, the round could have kept going by picking out a particular F-16, say the one flew by so and so in some particular mission or whatever.