Logic Puzzles - Admittedly, not naturally equipped to solve them...

A forum for good logic/math puzzles.

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Snarlock
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Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Snarlock » Wed Jul 27, 2016 2:44 pm UTC

I start by apologizing for perhaps starting a thread with a topic that is far below the standard level that is expected at a forum like xkcd.
My impression so far is that the far majority of users here are highly intelligent people, so I am hoping that perhaps you might shed some light on an issue that has bothered me forever.

I have MASSIVE problems solving logic puzzles. Unless I am given strong hints, I end up being stuck and cannot seem to naturally figure out the solution unless I obtain further knowledge through reading about logic on the Internet. To me, it seems like most people have a natural, raw intelligence that they are born with. They can solve these logic puzzles without being trained.

I feel like I am born with a rather low level of intelligence, and the only way for me to keep up with society is by having to learn. By that I mean, I cannot contribute to a debate or solve an issue unless I have any prior experience with or knowledge of the topic. The "raw" intelligence that other people possess, lets them be prepared for almost any logically solvable situation or issue that may arise, and knowing that I severly lack this skillset is bothering the hell out of me.

Reason for my concern is:
More than a year ago, two friends of mine came to visit, and while we were out for drinks one of them brought up the topic of logic puzzles. One puzzle was the famous "which of the two brothers is lying" and you were only allowed to ask one question to only one of them. The goal was to find out which path led to the favorable destination. The other friend came to the correct conclusion within 40 minutes of raw thinking.

It has currently been well over a year now and I have still not figured out correct question to ask. I refuse to take the easy way out and cheat by going online for the solution. I have met my "puzzle" friend two times since then and disappointed him twice by not being able to provide any questions that pass the criteria.

I ordered a logic puzzles book from the 80s called the "The Fantastic Book of Logic Puzzles", which is, as stated, aimed at teaching kids how to develop their logical thinking skills. The book starts with what it considers very easy, beginner level puzzles. You learn how to solve the puzzles one step at a time so that you are more prepared for the next difficulty level. It also comes with hints and solutions at the back of the book.

However, from the very start I am having difficulties without looking at the hints. This is at the absolute lowest difficulty level of logic, yet I spend a considerable amount of time before reaching a plausible solution. I am absolutely baffled that, as a grown man, I cannot even pass the basics of logic that are expected from kids in elementary school. I question myself if I am born with any logic intelligence whatsoever.

In a real life situation, I always rely on my social and body language reading skills when faced with a similar issue. Here again, this is presumably something you learn by experience rather than coming naturally. With these logic puzzles, I am totally stripped of this attribute.

I have never dared to test my intelligence by doing any IQ tests. I fear learning the truth! I barely passed mathematics, so that might be a pretty high indicator for my struggles.

Posting on an intelligent forum, I truly wonder about other users' experience with logic puzzles. Were you all naturally skilled or do most have to learn and lean on additional hints to reach a solution?

NB. Please do not post the solution in any of the replies. My dream is to slowly but surely figure this out myself :)

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Zohar » Wed Jul 27, 2016 3:56 pm UTC

I don't know if I was born with it, but math and logic were always interesting to me and I found enjoyment in doing them.

I'll start off by saying you sound intelligent - you have a rich vocabulary, you're clear, and you have a consistent voice. There are different kinds of intelligence, and maybe you're less talented in logical thinking and math, but so what? I mean, sure, you probably won't be an engineer without those skills. But you wrote yourself you're reasonable at reading body language and social cues, and you can express yourself. In logic puzzles, the answer has to be reached by logic. In real life, there are multiple ways to solve any problem or approach challenges, and if you prefer (and are better at) different ways, that doesn't say anything bad about you.

I could ask you different questions - are you good at games? How about board games? How is your memory? Can you learn how a system works and figure out things that are wrong with it? Ever tried programming? All are things that might indicate various levels of logical thinking. But instead I think it's more productive to ask, why is this important to you? If you enjoy thinking about logic puzzles then that's fine. But if you feel frustrated by them and they make you feel inferior to other people, then maybe you should try focusing on things that are more fulfilling for you. No person is the best at everything, and everyone finds challenges in some areas.

Take me for instance. I'm reasonable at math and logic, but I get exhausted in social situations which involve many people. The former might land me some types of jobs, but people can definitely handle life without those. Being comfortable in a party is arguably a lot more useful. You might be different, maybe - great at social interactions, can feel comfortable in many settings, etc. Or you have other areas you're better at.

It's easy to consider not being great at puzzles as a bad sign - it's simple to figure out how good you are at logic puzzles (Did you solve the puzzle? Did you solve it more quickly than others? Then you're pretty good!), and society likes easily-definable things. But it doesn't mean it's more important than other skills.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby ConMan » Wed Jul 27, 2016 11:32 pm UTC

I agree with Zohar - you sound like an intelligent person, just one who's more intelligent in what society considers "artsy" or "social" ways than "logical" ones. And I think it's admirable that you *want* to improve your logical skills, just like I want to be better at understanding social situations and managing things, and definitely one of the best ways to do that is to get lots of practice.

There are several aspects to logic, and I wonder if you've looked at some of those? For example, a lot of logic puzzles such as sudoku and grid puzzles invoke deductive logic - given a set of existing premises, what else must be true? Those ones can provide some semi-decent practice because in the worst case you can potentially brute-force parts of the solution by contradiction ("Let's assume the right answer is A. Then I keep filling things in until I realise I've broken something. Therefore the answer can't be A. Let's assume that it's B. Then I keep filling things in ...").

As for the two brothers puzzle, while you don't want the answer spoiled, are you interested in a hint? I can post one in a spoiler if you'd like, and others who read the thread can check whether it's a fair one before you try reading it.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Xias » Thu Jul 28, 2016 3:18 am UTC

I think you can be a wonderfully logical and intelligent person, and still struggle with logic puzzles because logic puzzles almost use their own language and rules. If you spoke the language, you would have little difficulty solving the simple puzzles, and the more challenging puzzles would only tease you for a bit.

Let's take Sudoku, for instance, since ConMan already brought it up. There's the stated rule: Each row, column, and square must contain exactly 1-9. From there you know that a number can't be repeated in any row, column, or square. However, if you sit down with a sudoku and just try to find numbers that fit, you're going to have a hard time. It's not until you understand that solving sudoku isn't about finding where stuff can go, it's about finding where numbers can't go. A person completely inexperienced with Sudoku may not come to that conclusion immediately, regardless of how smart they are. Even once you know that, there are only a few intuitive ways to know where stuff can't go, and the more experience you have the more patterns you see. The language of sudoku is how the placement of numbers tells you where new numbers must go.

So don't sweat that you haven't learned the language yet.

My advice is to first get a basic grasp of Propositional Logic, if you haven't already. You may need to take a course, or find an introductory textbook or something. Really get into it. The use of logical statements and operators and all that isn't really necessary for a lot of puzzles, but the way you have to think about statements is really useful.

Once you have the hang of propositional logic, Knights and Knaves are very simple puzzles that can be translated directly into logical statements, or solved through trial and error. I think these may be a great place to start, in terms of logic puzzles, and may help you train your brain to solve the Lying Brother puzzle. When you're comfortable with the Knights and Knaves format, you can even try coming up with some of your own.

When you finally do solve the Lying Brother puzzle - and I know you will! - try looking through this forum for variants. One of my favorites is the Three Princesses variant. You can check it out now, just don't read any of the replies because they may spoil the Lying Brother puzzle for you.

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby addams » Thu Jul 28, 2016 3:51 pm UTC

Snarlock wrote:NB. Please do not post the solution in any of the replies. My dream is to slowly but surely figure this out myself :)

You said, What??
ok. So DO NOT OPEN THIS LINK.
https://www.youtube.com/watch?v=ReFhu8KYbmU

We can discuss your post. Right?
I feel like I am born with a rather low level of intelligence, and the only way for me to keep up with society is by having to learn.
By that I mean, I cannot contribute to a debate or solve an issue unless I have any prior experience with or knowledge of the topic.

The "raw" intelligence that other people possess,
lets them be prepared for almost any logically solvable situation or issue that may arise,

and knowing that I severly lack this skillset is bothering the hell out of me.

I cannot contribute to a debate or solve an issue unless I have any prior experience with or knowledge of the topic.

That is what an education is for.
You might be low IQ.
But; With a lot of Work on your part and a faculty that is both supportive and demanding;
You could polish up that brain of yours and be useful.

You want to solve the mysteries of the universe all by your self?
You want to be Euclides, Archimedes, Galileo and Feynman, too?

and knowing that I severely lack this skillset is bothering the hell out of me.

I lack that skill set, too. It bothered the Hell out of me, too.
I went to school, read the book and don't hang out in Logic Puzzles on the Forum.
This part of the Forum may be reserved for the Talented and Gifted in Logic and Puzzles.

I had to have the solutions explained to me.
I had to be told why the solutions works.

I'm sorry your deficiency bothers you so much.
You may Never figure it out on your own.

The study book for the MCAT may help.
https://en.wikipedia.org/wiki/Medical_C ... ssion_Test
Preparation[edit]
Like most standardized tests, there are a variety of preparatory materials and courses available.
The AAMC itself also offers a select few tests on their website.

Some students taking the MCAT use a test preparation company. Students who do not use these courses often rely on material from university text books, MCAT preparation books, sample tests, free web resources, and educational mobile applications (free/paid).

oh, Gee...
Back in the ... Old Daze there was one 15,000 page book.

If a person read and understood that book,
That person could read and pass the test.

That book gave solutions.
I had to have the solutions explained.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Snarlock » Fri Jul 29, 2016 1:31 pm UTC

Huge thanks for all the comments :) I will get back to everyone during the weekend or on Monday with a proper reply. I will definitely follow the tips and tricks that are presented. Excited!

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Tyndmyr » Fri Jul 29, 2016 3:16 pm UTC

Logic is a trainable skill like many others. People have different starting points for a great many things, but training can overcome them. So, don't sweat inborn talent all that much.

I'd suggest looking at formal logic classes and picking up the rules, provides a proper foundation for other stuff.

Then, start thinking about independent ways to test and utilize logic. A common problem people have is looking for ways to demonstrate the truth of an idea, for instance, and they often do not try to falsify it. This results in spending lots of time on a dead end. You can see some pretty amazing jumps in solution time by including tests to eliminate bad solutions rapidly.

Another winnowing method is to look at the most restrictive constraints first. A lot of logic puzzles have multiple requirements, and a large number of possible options, so the difficulty comes at least in part from sorting through them. Selecting the most difficult to satisfy requirements first will give you a smaller solution pool to work with and greatly ease subsequent option picking, where this is possible.

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby jestingrabbit » Sat Jul 30, 2016 3:06 pm UTC

I think what you are doing right now, Snarlock, has aspects that are really sensible and admirable, but also parts that are deeply misguided.

The big problem I see here is mindset. You seem to have what's called a fixed mindset. What is better for you, your kids, and everyone else, is a growth mindset. As someone who has held themselves back with a fixed mindset for a long time, I want to free you from this burden. Try reading this article and internalising it.

http://www.opencolleges.edu.au/informed ... h-mindset/

What its saying, briefly, is that struggling is growth, and when you're struggling you shouldn't see it as a negative about you, but as an opportunity to grow and learn. But seriously, read the whole thing. Its good.

Secondly, in terms of this particular skill, lets go through a specific example. Lets talk about the first thing in the book that you're having trouble with. Lets start right there.

[I would ask that people that want to participate in this discussion to think about how they can engage with it productively before they post. I think its been going great so far, but lets not be arseholes. I put it in read so you would know that I mean it.]
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Snarlock » Mon Aug 01, 2016 11:03 am UTC

Zohar wrote:I could ask you different questions - are you good at games? How about board games? How is your memory? Can you learn how a system works and figure out things that are wrong with it?


Hi Zohar, thank you for the encouraging words. Your description of me is pretty much spot on. I would consider myself reasonably strong at video games, and what might surprise you is the fact that pattern recognition, spatial measurement and memorization happen to be my stronghold in games. It does not hurt that I possess rather quick and accurate “input” skills, but I gather that to be more of a physical trait.

I play very “morally”. By this I mean that my style of play tends to be solid, reliable in contrast to creative and risky. I.e., I rely heavily on a logical playstyle! The reason for this is simple. In games, I can always trust the laws and physics presented. What works one time is more or less guaranteed to work when repeated in the exact same situation. Consequences for my actions are always clear. However, in real life, I feel the opposite and insecure because I do not have faith that the same behavior is guaranteed to lead to a favorable result for all parties involved. I do not “trust” life the same way I do video games. Thus, I am forced to look at every situation individually rather than having a black and white mindset when making a decision.

So why am I bothered about not being particularly strong with logics? Well, the truth is, intelligent people who I admire and have met in a social and business related situation tend to all share one particular thing in common: a sound, logical thinking.

I will get back to the other posters soon!

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby quantropy » Mon Aug 01, 2016 12:47 pm UTC

Snarlock wrote: I play very “morally”. By this I mean that my style of play tends to be solid, reliable in contrast to creative and risky. I.e., I rely heavily on a logical playstyle!

I can't help thinking that you don't so much lack logical thinking as experience some unease with the idea that logical puzzles are trick questions (which is what they generally are). Some people enjoy logical puzzles for the 'aha' moment of realising what the trick is, but others might think that the answer is not really valid.

As an example there's puzzle 2 of the "Fantastic Book of Logic Puzzles". - I've had a look at the preview on google books. Here an astronaut on Mars puts 3 types of rocks (call them A, B and C) in 3 bags, but in his haste mislabels all of the bags. How many of the bags does he have to reopen to relabel the bags correctly. I've spoilered my analysis, but I hope that you'll take a look - it doesn't involve any of the liar/truthteller concepts which are in the puzzle you mentioned
Spoiler:
Well the most sensible thing seems to be to reopen all of the bags, since if he has made a mistake, he wants to be fairly sure he gets it right. However, once he has opened 2 of the bags, he will know what is in the third, so only 2 are needed.

But the puzzle says he mislabelled all of the bags. This means that if they are labelled A, B and C then the only options are that they contain B, C and A respectively or C, A and B. This means that he only needs to open one bag to find out which.

Is this a valid answer though? The puzzle says he mislabelled the bags in haste, which would really imply that he didn't know whether each bag was labelled correctly or not. This would imply that the answer isn't valid.

I couldn't read the answer in the book preview, so I don't know what it has to say (or I might have got the wrong idea of what the question was asking for). But I do feel that this shows that the answer may well depend on what you consider valid

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Snarlock » Mon Aug 01, 2016 1:42 pm UTC

quantropy wrote:As an example there's puzzle 2 of the "Fantastic Book of Logic Puzzles". - I've had a look at the preview on google books. Here an astronaut on Mars puts 3 types of rocks (call them A, B and C) in 3 bags, but in his haste mislabels all of the bags. How many of the bags does he have to reopen to relabel the bags correctly. I've spoilered my analysis, but I hope that you'll take a look - it doesn't involve any of the liar/truthteller concepts which are in the puzzle you mentioned


Hi! Funny you should mention this particular puzzle. I remember failing at it :( I did not look at the hints in the back of the book because I thought I had the answer. Sadly, no...

However, I thought it was an entertaining puzzle which I definitely learned from, and I am happy to now be more prepared for a similar puzzle in the future. Still, I felt it a little discouraging when realizing how my method of thinking just did not fit the bill.

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Snarlock » Tue Aug 02, 2016 9:29 am UTC

ConMan wrote:There are several aspects to logic, and I wonder if you've looked at some of those? For example, a lot of logic puzzles such as sudoku and grid puzzles invoke deductive logic - given a set of existing premises, what else must be true? Those ones can provide some semi-decent practice because in the worst case you can potentially brute-force parts of the solution by contradiction ("Let's assume the right answer is A. Then I keep filling things in until I realize I've broken something. Therefore the answer can't be A. Let's assume that it's B. Then I keep filling things in ...").


Thank you, ConMan. I actually really enjoy Sudoku but have not attempted my fate at other grid puzzles yet. Maybe you can introduce me to some? What I like about Sudoku is that you can learn patterns that are both easy to recognize as well as trickier. Solving a small piece gets you closer to solving a bigger piece. It is a great substitute to video games :)

However, Sudoku was something I had to learn and I only got better with massive amounts of practice. To me, in the beginning at least, I felt like I was getting by mostly by trial and error rather than pure logical thinking. I always play the hardest Sudoku levels and currently pass around half of them successfully. For the ones I get stuck at, I go online to learn new patterns and techniques. When I see other Sudoku puzzlers somewhere in public, I always assume that these people are smart. With me however, knowing that I am personally only staying afloat due to having memorized these Sudoku techniques, I know that I am only fooling myself into believing I am somewhat intelligent.

Xias wrote:It's not until you understand that solving sudoku isn't about finding where stuff can go, it's about finding where numbers can't go. A person completely inexperienced with Sudoku may not come to that conclusion immediately, regardless of how smart they are. Even once you know that, there are only a few intuitive ways to know where stuff can't go, and the more experience you have the more patterns you see. The language of sudoku is how the placement of numbers tells you where new numbers must go.


Hi there Xias. Yes, the techniques I have learned do just that. They eliminate possibilities and gets me closer to placing the appropriate numbers :) Thank you for your post and links provided. By your help I feel like I am heading in the right direction. I will begin on the path you suggested.

Tyndmyr wrote:A common problem people have is looking for ways to demonstrate the truth of an idea, for instance, and they often do not try to falsify it. This results in spending lots of time on a dead end. You can see some pretty amazing jumps in solution time by including tests to eliminate bad solutions rapidly.


Am I beginning to seeing a pattern here? Similarly to Sudoku, rather than looking for WHERE a number should go, I should focus on where it SHOULD NOT. Should my steps with logic thinking/puzzles in general be to always determine which paths or ideas are false, eliminating the false possibilities one step at a time? There was one or perhaps even two puzzles in the "Fantastic Book of Logic Puzzles" that I did managed to solve without needing hints. There were three groups of creatures that had specific traits, and in order to solve the puzzle I had to eliminate one group at a time based on certain characteristics that were only true to one of the groups.

ConMan wrote:As for the two brothers puzzle, while you don't want the answer spoiled, are you interested in a hint? I can post one in a spoiler if you'd like, and others who read the thread can check whether it's a fair one before you try reading it.


I will try a little further and get back to you if necessary :)

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby SteelCamel » Tue Aug 02, 2016 9:04 pm UTC

Am I beginning to seeing a pattern here? Similarly to Sudoku, rather than looking for WHERE a number should go, I should focus on where it SHOULD NOT. Should my steps with logic thinking/puzzles in general be to always determine which paths or ideas are false, eliminating the false possibilities one step at a time?


Yes, that's often important. Going back to Knights and Knaves, you know the puzzle has a solution, so you know you can find out what road to take. But if you think about what you cannot find out, you may see a way to the solution.

If you want me to expand that (fairly cryptic hint but possible spoiler):
Spoiler:
You can ask one question, and find out one thing. That one thing must be "Which road is the right way?". What you cannot find out is absolutely everything apart from this. If you think that knowing the correct road requires finding out something else first (or at the same time), you are wrong - the problem construction does not allow it. If you now see what you cannot do, you should be able to work out what you must do.

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Sizik » Wed Aug 03, 2016 12:22 am UTC

Have you ever done logic grid puzzles? They're pretty similar to sudoku, except a bit more wordy.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby ConMan » Wed Aug 03, 2016 1:30 am UTC

Snarlock wrote:
ConMan wrote:There are several aspects to logic, and I wonder if you've looked at some of those? For example, a lot of logic puzzles such as sudoku and grid puzzles invoke deductive logic - given a set of existing premises, what else must be true? Those ones can provide some semi-decent practice because in the worst case you can potentially brute-force parts of the solution by contradiction ("Let's assume the right answer is A. Then I keep filling things in until I realize I've broken something. Therefore the answer can't be A. Let's assume that it's B. Then I keep filling things in ...").


Thank you, ConMan. I actually really enjoy Sudoku but have not attempted my fate at other grid puzzles yet. Maybe you can introduce me to some? What I like about Sudoku is that you can learn patterns that are both easy to recognize as well as trickier. Solving a small piece gets you closer to solving a bigger piece. It is a great substitute to video games :)


Honestly, a large amount of logic is about learning patterns, then learning how to apply them (or the methods used to determine them) to other problems. For example, there's been discussion in this thread about how a lot of Sudoku is about flipping between "what numbers can go here", "where can this number go", "what numbers *can't* go here" and "where *can't* this number go" - in other words, finding alternative perspectives to the problem that increase your information about it. That's a great skill, and it's applicable in many other circumstances (for example, in a jigsaw puzzle, you can speed things up by being able to recognise which pieces aren't useful to you at the moment, so you can focus on the ones that might be directly usable).

If you're interested in trying out puzzles that use similar kinds of logic to sudoku, I'll recommend the Nikoli website, where there are a lot of different types of logic-based puzzles, some of them trickier than others (I still can't do big Numberlink puzzles personally, but I love Masyu and Yajilin). You could also look up the puzzles that are known in various areas as "nonograms", "picross" and "pixel puzzles", which have the benefit that when you get the puzzle right you're rewarded with a picture rather than a grid filled with numbers.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby HokieNerd » Wed Aug 10, 2016 1:20 pm UTC

Snarlock wrote:I actually really enjoy Sudoku but have not attempted my fate at other grid puzzles yet. Maybe you can introduce me to some? What I like about Sudoku is that you can learn patterns that are both easy to recognize as well as trickier. Solving a small piece gets you closer to solving a bigger piece. It is a great substitute to video games :)


If you're still looking for another grid puzzle to practice pattern recognition tricks, might I suggest Kakuro? It's another numerical grid puzzle, yet tied to sums rather than specific digits in a row/column. I enjoyed that game much more than Kakuro.

I wish you the best of luck in your quest for logical knowledge. While I enjoy logic puzzles, and am decent at them, I don't have near as much time to play at them as I as I want. Maybe if I can trade one of my two kids for another logic puzzle book..... ;^)

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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby Goahead52 » Thu Aug 11, 2016 12:34 am UTC

Do not worry about IQ (low or high is not important) because solving puzzles has nothing to do with IQ. I have seen people solving hard puzzles only because they worked hard to know some tricks to recognize some patterns and so on. The same prevail with chess game. I have seen "dumb" people (I do not like this word even if I used it) becoming masters in chess game only because they have good memory and they played lot. Dumb means that people are not interested to learn that`s it.
As long as you have the will to solve puzzles even the hardest you will succeed if you read solutions understand them and you try to classify all the kinds of puzzles. Many puzzles need focusing on what is the breach to attack to solve. Each puzzle could be compared to a house : if you try to enter to by using the door keep in mind anyone will try the door first. Try the windows, the chimeney, the backyard and so on until you find the correct way to go inside the house. Try and try until you find the solution. But try before going to the given solution. But once you read the solution try to understand it and to create similar puzzle (some sort of variant) by changing some parameters by generalizing them etc...
Anyway I wish good luck.
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Re: Logic Puzzles - Admittedly, not naturally equipped to solve them...

Postby ThirdParty » Sat Aug 27, 2016 4:10 pm UTC

I think it's fair to say that everyone who does logic puzzles has gotten stuck at some point, and used a hint or even looked up an answer. Not everyone will have gotten stuck on this particular puzzle, but everyone will have gotten stuck on some puzzle or other. Getting stuck doesn't reflect on how naturally-talented or generally-intelligent you are; everyone gets stuck.

The same is true of learning to read, or learning to program computers, or learning to golf. Whatever the skill in question is, there will be stages in your development of that skill where you need a hand from someone else in order to progress.

Luckily, there are hundreds of thousands of interesting logic puzzles out there. Even if you end up having to use a spoiler for Puzzle #1, you'll still be able to have the satisfaction of solving Puzzle #2 unaided.


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