[HN Gopher] Coming to Agreement, a logic puzzle for Oxford admis...
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Coming to Agreement, a logic puzzle for Oxford admissions
interviews
Author : mathgenius
Score : 26 points
Date : 2021-12-27 21:43 UTC (1 hours ago)
(HTM) web link (jdh.hamkins.org)
(TXT) w3m dump (jdh.hamkins.org)
| curiousgal wrote:
| > _Some student candidates had proposed an interesting idea of
| trying to blend the two colors. [...] I like this idea a lot, but
| it seems problematic in light of the fact that we don't have such
| a clear and unambiguous means of combining colors._
|
| Not if we use RGB, send the color as a tuple of three numbers and
| average both tuples (taking the floor for example if one of the
| numbers is odd).
| scatters wrote:
| How would you know to use RGB and not CMYK or HSL?
| goldcd wrote:
| There's solving the problem - and there's solving the scenario.
|
| I'd presume that a logical contestant would google blue to be the
| most frequently chosen random colour, and the two of you would
| just scream "blue" at each other other and then you'd end the
| game.
| nkmnz wrote:
| This is not true in a live and death scenario, because with
| asymmetric payoffs like that - termination being the down side
| risk - it is not at all ,,rational" to jump to the answer that
| gives the highest probability of success, if that answer still
| has a non-zero risk of death.
| goldcd wrote:
| Then as I mentioned below, you neither of you send a message
| and the game remains open indefinitely.
| nkmnz wrote:
| How do you do that after you've been killed for screaming
| ,,blue"?
| throwaway73838 wrote:
| One of the difficulties is deciding on a strategy that would work
| even if the other player used the exact same strategy on you.
|
| My solution is to say something like: 'I will nominate a colour
| next round. If we both nominate the same colour, I will say that
| colour and end the game next round. If anything else, I will
| nominate a different colour, proceeding alphabetically.'
|
| Of course, it would depend on what message you receive that round
| - there's probably no one size fits all approach, such as the
| issues of both people using an unyielding strategy. So maybe
| you'd have a clause which says, if the other player gives an
| ultimatum message, then you will go along with that.
|
| I don't think there's a perfect solution here, but I could be
| wrong.
| kaz_sadeghi wrote:
| I'm surprised more people didn't recognize the two generals
| problem.
| nkmnz wrote:
| It's not the two generals problem because you can be sure that
| your companion gets the message (both literally a d
| figuratively). The two generals problem is about inherent
| uncertainty, while the given problem has full transparency.
| josephcsible wrote:
| But isn't that exactly what the "Pigeon variation" the
| article mentions is?
| Someone wrote:
| FTA: We had used these puzzles in our admissions interviews of
| candidates for a place at Oxford University in the degree
| courses Math/philosophy, CS/philosophy, and PPE at University
| College, Oxford
|
| I'm not familiar with the term "degree course", but suspect the
| candidates were bright, but also around 18 years old.
| tylerhou wrote:
| These are probably admissions for high schoolers.
| nkmnz wrote:
| ,,Imagine the stakes are very high--perhaps life and death."
|
| The only acceptable solution for perfectly rational players in
| the case of ,,death" as possible down side while only having
| ,,live" as a potential upside would be to extend the game
| indefinitely by telling the co-player that you will never agree
| on a different strategy than infinite play - all possible
| rewards, zero downside risk!
|
| Where can I get my ticket to Oxford?
| goldcd wrote:
| Well in that case, you just don't answer. Your buddy on the
| other side also wouldn't be expecting you to, so they'll just
| leave the game running indefinitely as well.
| nkmnz wrote:
| Exactly. Asymmetric payoffs lead to strange behavior.
| [deleted]
| Fellshard wrote:
| Consensus protocols 101? It seems to boil down to, 'who will
| subordinate' - it doesn't matter who, so long as someone does.
| There is a risk of interminably failing to come to consensus on a
| means for finding consensus, though, an infinite regression that
| would necessarily need to be broken by one or the other...
| GenerocUsername wrote:
| These puzzles would make horrible college admissions tests. They
| hardly qualify as interview questions.
|
| This typpe of problem is nearly impossible for folks that have
| never heard a similar test and nearly trivial for someone who has
| heard ~3 like it.
| rndm_access wrote:
| This is general problem with modern public founded education
| system - it prizes memorization of repetitive schemes - as it's
| easy to check on the mass scale who is able to memorize these
| schemes. It's several magnitudes harder to check who really is
| a material for a scientist among same large population of
| candidates. I was educated in top university in my Central
| European country and to this day cannot shake off memories of
| people who passed calculus exams by memorizing solutions of
| integrals instead of understanding how to solve them. It was a
| general scheme - mediocre students interested only in "getting
| paper" aka diploma were passing exams mostly flawless some of
| them even get scholarships[sic(k)!] while people interested in
| actually understanding material and doing projects by their own
| (most students were making projects in groups and changing only
| minor details and teachers were pretending they do not see
| that) were struggling within that system. As the system has
| memorization without understanding and cheating as a
| fundamental of it's construction and people who resist
| following that pathological scheme were simply penalized.
| Attempts to rationalize with academic teachers in many cases
| resulted in absurd remarks of "everyone have equal requirements
| for passing classes". Puke inducing every time I think about
| that.
| aardvark179 wrote:
| They were used for interviews for maths and CS, so I think it's
| quite likely the candidates would have seen similar puzzles
| before, but I think that misses the point. This sort of puzzle
| is there so that the students can either present and an answer
| and the interviewer can start to dig into it with more
| questions, or so that the candidate doesn't come up with an
| answer immediately and the interviewer can ask other questions
| that will help them reason things out.
|
| The object is generally to explore how a candidate thinks. If
| it turns out they memorised logic puzzles and can't explain
| them then they will not get through the interview.
| jonsen wrote:
| Apparently it's neither intended nor used as an
| "impossible/trivial" problem:
|
| _The interviews were an in-depth back-and-forth discussion, as
| much as could be had in about 25 minutes. These interviews, of
| course, are just one component among many in regard to the
| difficult admissions decision, a chance for the candidate to
| show us how they think through a problem, how well they can
| explain their ideas, how well they take hints and suggestions.
| In every interview, we had paused at a certain stage, when the
| candidate had a fully formed argument for one of the
| variations, and asked them to undertake an integrative
| exercise, summarizing as clearly as they could the entire
| problem and solution and how they expected it to play out.
| Since these were interviews for joint philosophy degrees, in my
| view this step was a key part of the interview, measuring the
| ability of the candidate to integrate what they had learned
| from the discussion and to present a complete, coherent
| argument._
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