Yeah, I get it now. I definitely was assuming that, but I see that it wasn’t actually implied in the scenario. I brought in my own assumptions about cards. The idea that each card is unique didn’t occur to me because if they actually were unique then the rule in question couldn’t be true regardless based on what we see. But they could be e.g. an arbitrary mix of uniques and duplicates.
Have you learned about formal/mathematical logic before? Had you heard about necessary and sufficient conditions?
I’m asking because I think making assumptions that the numbers and letters are arbitrary and that there could be duplicates is a lot more typical for programmers/mathematicians/logicians etc. to make. Maybe I should specify more about the general card generation rules, I’m not sure.
Yeah, some.
Maybe. I have learned some programming in the past but haven’t used it in many years.
I think specifying too many rules will make people less likely to fail, but I think a test like this is intended to make people fail to demonstrate that people often fail logic puzzles due to bringing in their own assumptions, so that seems counterproductive?
I finally watched the video (well, just the beginning so far) after we discussed the scenario.
The pub version did immediately seem more intuitive. Like, I think there is no chance I would have failed that one, and I’m not surprised most people don’t.
I suspect one reason could be because it decouples any assumptions I might have about card manufacturing/uniqueness/duplication/etc. from the scenario. Once the card faces just represent current people & current drinks basically everyone will intuitively know that the options can be any arbitrary mix of possible duplicates, all unique, etc.
Good suggestion. I don’t the think the other explanations given like our reason being develop for “social reasoning” is correct. I thought it had to be something like people are actually gaining more information when given the question in a social context. I couldn’t explain that though if it was really just applied to social contexts rather than object contexts like “is raining” and “grass is wet” (that wouldn’t be a great example because it raining doesn’t actually guarantee the grass is wet in reality). It could be people have more implicit knowledge about social rules than other things.
What? Duplicates are possible. For example, the visible A could have a 7 on the other side, and the visible 7 could have an A on the other side.
I don’t think that’s correct. Do you still think this after the additional clarifications and stuff later in the topic?
Most people are bad with variables and algebra. One reason is they aren’t good at remembering arbitrary letters or numbers.
Lots of people can remember the names of 10 Taylor Swift songs but remembering 10 digits of pi sounds extraordinarily difficult to them. This is despite a song name containing more information than a digit and therefore being, in some sense, harder to remember. You do have to remember the digits in order, but I believe some people remember all the song titles from one album in order. (This example may be dated. I’m not sure how much people care about track order today now that they tend to listen on iTunes or Spotify instead of with physical media.) Also some those same people remember a bunch of phone numbers.
So, for example, if you write a philosophy essay with a hypothetical scenario about person A and person B, many readers struggle. If you instead name them Alice and Bob, some readers do better. Or so I’m told. This is not intuitive to me personally.
People are used to remembering names and associating traits with names. Also lots of people use visual memory, so they can imagine what they think Alice and Bob look like, whereas they don’t visualize plain letters and numbers well.
Also many people are scared of algebra/math, had bad experiences in school, and avoid thinking about it. Just seeing A and B (let alone 7 and 8) can bring that up.
Also, if I read Alice and Bob, I might rename them A and B in my head. But a lot of people who prefer Alice and Bob won’t rename them from A and B. I think people are more likely to rename to rather than from single-letter variables. Renaming to short variables is the much more conventional direction and there may be other reasons for the asymmetry.
These issues with memory and math are my first guess about why people struggle with the cards over the pub.
I’m initially/intuitively skeptical that many people are confused about uniqueness and duplication stuff with cards. Though maybe calling them pieces of paper would have been better.
That’s right. I’m not sure why I thought that.
Edit: Actually, I’m a bit sleep deprived, that’s probably why. I still find the mistake perplexing given what I knew and thought about the question just before that.
The song names will likely follow a single theme whereas the digits of pi has no pattern. Maybe you could know how to calculate pi and “remember” it by using calculation shortcuts to fill in blanks.
I think the names following a theme makes it easier to remember because it limits what are plausible names and lets you maybe remember a part of the name and that helps you remember the rest.
Popper does label things alphanumerically often and I often have to go back to reread which was which when he refers to them in the text.
I’m not sure about uniqueness and duplication either but I think it being about assumptions generally is a part of it.
No, I was incorrect. You could have A+7, G+5, Þ+7, G+8 — every card there is unique. I think I was still confused about what options you could have, or I was still failing to think about the rule only going one way, or something.
Yeah maybe it’s not about the card stuff I theorized earlier. I don’t really know why I struggled with it. I was tired when I posted earlier, but even now when I am not feeling as tired there is something about it that I find difficult. And I find it difficult to articulate my thought process from before.
I don’t generally find examples with “Person A” and “Person B” difficult to follow. Personalizing them with names might help me track a scenario slightly better but not by a lot, I don’t think. On the other hand, for me it is a lot more difficult to memorize long sequences of numbers than it is to memorize much longer sequences of words.
In general I find it easier to remember things I care about, find interesting, etc. That includes lots more words than numbers, though when numbers fit that criteria I think I remember them pretty well. I still remember the rules for tabletop games I haven’t played in many years (including associated numbers, e.g. I am pretty sure that in AD&D Strength 18/00 grants +3 to hit and +6 damage even though I have not played that edition in a long time) — but I do not remember any mathematics rules that I learned that long ago have not used in a similar time.
So that’s sort of a messy jumble of ways your theory applies to me and doesn’t apply. Does this explain why I was confused at first? Maybe, I dunno. Not convinced it does, but not necessarily convinced it doesn’t, either.
It kinda seems like I just did not process the actual rule correctly, and was too caught up on the fact that cards are set objects (which is actually irrelevant but seems to have felt relevant based on my initial comment). Like I just sloppily treated the rule as “cards have that have A on one side have 7 on the other side and vice versa” even though it doesn’t say that at all. IDK why I would have made that assumption, though. I don’t think I usually make that kind of assumption when presented with logic puzzles. That’s why I theorized it was something about them being described as cards that tripped me up. But I am not super confident in that guess.
I was distracted when I read this and came up with an answer yesterday. I ended up getting it wrong. I don’t know if I would have gotten it right if I focused on the question more, but it’s interesting that my instinct without thinking hard about it was to flip A and to flip 7.
The younger me would feel bad about getting this kind of question wrong, but now I enjoy figuring out where I made a mistake. It helps me understand where I can improve.
Is it just me or should the question have been written better/more precisely? I think people who write these kinds of aptitude questions should be held to a high standard. Like they tend to reward people who give a more conventional answer rather than those who are thinking less conventionally or who may be taking the question more literally.
The “must you flip” part bothers me because it depends on if you’re thinking about the complete plan before the cards are flipped or which cards will actually physically need to be flipped during the attempt. During your attempt, if you flip the A and and an 8 appears, the rule is broken. So you know the rule is false and you don’t have to flip the 8.
Also “ determine whether the following rule is true” feels too broad…
Yeah I thought about this too. Depending on the results, you can stop after fewer flips. So I took the problem as you have to decide all your flips at the outset. Or you have to count the maximum (not e.g. average) number of flips your plan uses aka the worst case scenario. They could have specified it more clearly.
Do you have a good sense of why your initial intuition was wrong? Mine was also wrong, and I’ve posted some guesses as to why, but I don’t have particularly high confidence in those guesses.
I also didn’t mind being wrong, and like you I think I might have felt worse about it when I was younger. But I think for me it has less to do with thinking about it as an area I can improve (since I don’t fully know why I made the mistake in the first place) and more to do with having different priorities and less sense of self-importance.
But if you have more guesses I’d be happy to see them, since there’s a chance we could have overlap.