20 questions: Will anyone guess my favorite number by the end of January?
14
18
270
resolved Jan 5
Resolved
YES

Inspired by this market, and this one.

I have a favorite number. It's a number that is in some sense "interesting", so it's feasible for people to guess. (Though opinions can differ on the interestingness of a certain number.) Note that my definition of "number" for the purposes of this market is very loose, so it might include things you wouldn't normally consider to be numbers.

Each user gets to ask one YES or NO question about my favorite number, which I will answer honestly.

If their question was "is it [number]?" and the answer is yes, then I'll manalink that person M$50 and resolve the market to YES. Otherwise it resolves NO at the beginning of February.

(Any questions attempting to use this to divine other information, such as "is the first digit of your favorite number the same as the first digit of your credit card number?" will be disqualified. Any questions that are too hard for me to answer are also invalid.)

(There's no 20-question limit, that's just the traditional name of this game. It's one question per user.)

Here's is a list of all questions that have been asked so far and their answers:

  • Alana: "Is it 69?" No.

  • Elspeth: "Is it a member of the set of complex numbers?" Yes.

  • Elspeth [allowed due to error on my part]: "Is it a member of the set of complex numbers and have both a nonzero imaginary portion and a nonzero real portion?" No.

  • Jacknaut: "Is it listed on https://en.wikipedia.org/wiki/List_of_numbers?" Yes.

  • NeonNuke: "Is it an integer?" No.

  • Josh: "In that Wikipedia list, is it under either 'Numbers representing physical quanties' or 'Transfinite numbers'?" No.

  • Martin Randall: "Is it a real number?" Yes.

  • Moneylab: "Is it pi?" No.

  • Levi Finkelstein: "is it in the set [Φ, sqrt(2), tau, e, ln 2]?" No.

  • Tassilo Neubauer: "Is it in the interval (0,1)?" Yes.

  • Heliscone: "Is it listed under section 5 of the Wikipedia list?" No.

  • muffins: "Is it listed under section 6.1 of the Wikipedia list?" No.

Get Ṁ600 play money

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predicted YES

By the way, I don't like how my favorite number is actually a class of numbers. Anyone wanna point me to a specific construction that's unique in some way?

predicted YES

Not sure if I get a second question since the first was invalid. If so, is it 3rd Landau’s constant?

predicted YES

You do get another question, but Scott just got the answer. It's Chaitin's constant(s).

Each user gets to ask one YES or NO question about my favorite number, which I will answer honestly.

Are you included in the set of users who can ask a question?

predicted YES

@MartinRandall I guess technically I am, yes.

Is it Chaitin's constant?

predicted YES

@ScottLawrence Yep! Are you on Discord? I'll PM you a manalink.

@IsaacKing Just created a discord account. (Maybe I had one? But I can't find it.) My username is slawrence. I'll PM you.

Damn, I considered asking this, but decided that you were probably just glomarizing.

predicted YES

@Yev Haha, glomarization successful!

bought Ṁ50 of YES

Also I've made a sequel with a number of slight rule changes:

predicted YES

Is it under section 6.1 of the Wikipedia list? ("Real but not known to be irrational, nor transcendental")

predicted YES
predicted YES

Is your number in the interval (0.6,1)?

I don't think this is a valid question. It is too hard to answer if Isaac's favorite number is Chaitin's constant or 3rd Landau constant.

I think a better question would be "Is your number known to be in the interval (0.6,1)?" (Note that I am not asking this question, so it should not count towards my question limit)

@JimHays This question is invalid.

11 questions asked so far. Will it be guessed before we get to 20? (I predict yes.)

bought Ṁ20 of YES

In that wikipedia list, is your number listed under "Algebraic numbers," "Transcendental numbers," or "Irrational but not known to be transcendental" [section 5]?

Is your number in the interval (0,1)?

predicted YES

Levi has made me realize that I need to have a rule against questions that are too hard to answer. "Is any integer multiple of your number a zero of he Riemann zeta function?" would not be a valid question. :)

@IsaacKing Why? We already figure out that your number is real. And the real roots of the Riemann zeta function are well behaved (even negative integers). I think this question is equivalent to asking whether your number is rational.

bought Ṁ10 of YES

@Yev My take would be that “too hard” is relative and distinct from “impossible”, so this restriction can prevent needing to do unnecessary computation or proof if a question is difficult, but might be computable