Serious Brain Teaser
This one has been doing the rounds this morning, so I couldn’t resist posting it here:
PS. If anyone knows where this originated please let me know and I’ll give proper credit!
PPS. Note that the Mike Disney option (300%) is missing…
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In the Dark 
October 28, 2011 at 11:36 am
Very likely from Richard Wiseman.
October 28, 2011 at 2:05 pm
or rather from @jbrownridge who Wiseman says sent it to him
October 28, 2011 at 12:40 pm
Or possibly David Spiegelhalter, difficult to tell who came first?
October 28, 2011 at 2:13 pm
Is it ⊥ ?
October 28, 2011 at 2:15 pm
The correct answer is of course Coventry City, in 1987.
October 28, 2011 at 2:21 pm
Or is it ⋊ ?
Such a circular argument that my pinic table has fallen over (to the right)
Yes, Richard Wiseman it appears – I saw it at about 8am from @ColinTheMathmo
October 28, 2011 at 3:13 pm
The correct answer to this question clearly depends on what the correct answer actually is.
October 28, 2011 at 3:23 pm
.. After a little thought, it has to be a toss-up between A and D.
October 28, 2011 at 4:24 pm
What’s the answer to this question?
October 28, 2011 at 4:28 pm
“this” refers to my question
October 28, 2011 at 4:49 pm
Do you mean what is the question to which what is the answer?
October 28, 2011 at 5:11 pm
Well said Jim, that’s exactly what’s going on. Substitute it back in, to get:
What is the answer to the question: “What is the answer to this question?”
And so on.
October 28, 2011 at 5:12 pm
MORNINGTON CRESCENT!
October 28, 2011 at 5:14 pm
A more interesting question is what are the little black rectangles all over the chalkboard?
October 28, 2011 at 5:17 pm
Is this a question?
October 28, 2011 at 5:56 pm
Is the question some form of “logical fallacy” ?
An existential one perhaps ? I’m in the dark.
More topically, if a FTSE 100 executive choses a pay increase at random (say >49%), what’s the probability the executive think’s they are right? a) 100%, b) 100%, c) 100%, d) 100%
October 28, 2011 at 10:07 pm
original source?
https://plus.google.com/116264189418994838408/posts/CSXeyftovTJ
By the way, I set up a quick simulation of the problem:
make a random pick 1-4, ask: does the look up value match – to within a small error – the cumulative frequency of all previous random picks?, then add a 1 or 0 to the stack for True/False and calculate the new (n+1)th cumulative frequency, then let the simulation run until a large number (N) of iterations is reached.
The results, plotted vs. iteration number (n), quickly settled into bi-stable alternation, hoping between 25% and 50% – so no convergence. Pretty sweet.
October 29, 2011 at 11:11 am
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October 30, 2011 at 9:47 am
Very nice! After banging my head on the wall for some time, I came to the conclusion that there is an answer. Isn’t it zero? On the basis that none of the answers (a)-(d) is self-consistently correct.
An interesting variant is to change (d) to 50%. What is the answer now?
October 30, 2011 at 10:54 am
If the answer is 50% or 60%, you have a 25% chance of getting it; If the answer is 25%, you have a 50% chance of getting it. Trick question or, more likely, what am I missing?
:-S
October 31, 2011 at 1:57 am
This is Russell’s Paradox 110 years later. A set of numbers cannot be included as a member of it’s own set. So by listing 25% twice, the question basically makes the entire list of 4 answers a member of the set…basically a 5th answer which also contains an answer.
That paradox creates a logical loop because the set of 4 cannot also be one of the answers.
October 31, 2011 at 11:47 am
Yes. Jim nailed it above on October 28, 2011 at 4:24 pm (“what’s the answer to this question?”)
October 31, 2011 at 12:08 pm
Thinking about this problem again made me think (for some reason) of Turing’s famous Halting Problem and the so-called Doomsday argument.
The thing is that even using the proper Bayesian framework for generalising deductive logic to uncertain events is bound to fail if one is dealing with propositions which would be undecidable even with certain knowledge.
Must think about this a bit more.