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MarkT

WFG Retired
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  21. Rts Lovers

    in Introductions & Off-Topic Discussion

    Posted

    I like RTSes with a quality environment - music, art and so on... But, more than that, the thing that makes a good game great is a storyline - if it's something decently epic (eh, well... that's the Homeworld series, and Total Annihilation felt epic but didn't really use the story beyond the intro)

    First Topic - Riddles

    in Hall of Intellectuals

    Posted

    You have asked. So you shall recieve.

    mreiland is right, of course, it's not that complicated - unless of course you've studied rather too much mathematics, in which case you do this:

    Brace yourself... B)

    Twelve variables:

    J, A, M mean that John, Amanda or Mike has passed, respectively.

    JG, JN, JS: Ugly, Unique and Useful's statements to John were true.

    AG, AN, AS and

    MG, MN, MS: The judges' statements to Amanda and Mike were true.

    Then J = 0, or ~J = 1, both mean that John did not pass.

    'Facts' are written (J = 0): 'we know that John did not pass.'

    The symbol => is 'implies' (but >= is still greater-than or equal to...)

    The symbol <=> is 'implies and is implied by'

    Now:

    JN <=> J 'You passed'

    JG <=> ~JG + ~JN + ~JS >= 1 'At least one of us will lie to you'

    ~JG => JG therefore (JG = 1) - otherwise there'd be a paradox. Then,

    JG <=> ~JN + ~JS >= 1 - but,

    JS <=> JG 'U-gly spoke the truth' - so,

    JG <=> ~JN, and (JG = 1) therefore,

    (JG = 1), (JN = 0), (JS = 1), (J = 0)

    Having fun?

    Next:

    AG <=> ~A

    AN <=> JG + AG + MG = 0 'U-gly never speaks the truth' but

    (JG = 1) therefore (AN = 0)

    AS <=> ~AG + ~AN + ~AS >= 2 'At least two of use will lie to you' - but (AN = 0), so,

    AS <=> ~AG + ~AS >= 1 - now,

    ~AS => AS - therefore (AS = 1), to avoid the paradox,

    AS <=> ~AG >= 1, so (AG = 0), giving:

    (AG = 0), (AN = 0), (AS = 1), (A = 1)

    Finally (assuming U-gly was talking about U-seful):

    MG <=> MS 'U-seful will tell you the truth'

    MS <=> M + MN = 2 'You passed and U-nique told you the truth'

    MN given M <=> ~MG 'If you pass, U-gly lied to you'

    MS => M + ~MG = 2 - because if M, then MN <=> ~MG, but

    MS <=> MG - so

    MS => M = 2 - therefore (MS = 0)

    ~MS => M + MN <= 1 - then either

    M = 0 - or

    MN = 0 - but

    ~MS <=> ~MG <=> MN - which can't happen, therefore

    (M = 0)

    Otherwise, if U-gly was referring to U-nique:

    MG <=> MN 'U-nique will tell you the truth'

    MN given M <=> ~MG 'If you pass, U-gly lied to you' - then,

    MN given M <=> ~MN - therefore,

    (M = 0), to avoid the paradox.

    So (J = 0), (A = 1), (M = 0).

    All good fun, but someone else needs to check this. Is there a logician in the forum?

    First Topic - Riddles

    in Hall of Intellectuals

    Posted

    *cough* I'm admitting a stupid mistake. (Misread the question...)

    This time, at least, I have pages of notes that seem to indicate this is the correct answer:

    Amanda, and only Amanda, passed to the semi-final.

    However, my reasoning is now a sheet of fairly arcane algebra. Anyone else want a go, to save me having to translate it back into English?

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