Tips for solving logic problems quickly?

Detective Conan

Detective Conan

Doesn't Cast Shadows
MBTI
INFJ
Enneagram
2w1
G'day, forum, it's been a while since I've posted anything here. I was wondering if anyone here had tips or tricks on how to quickly and correctly solve logic problems. I've got some methods that work (drawing out a table or diagram usually works) already, but they aren't all that quick and thus ineffective, if not crippling, for the short time frame of a standard test.

If anyone has any ideas/advice/methods, I'd vastly appreciate it if you would kindly share them (as may others on the forum).

Here's a quick example of a logic problem where the diagraming method would eat up too much time (at least in my experience).

Of three prisoners in a certain jail, one had normal vision, the second had only one eye, and the third was completely blind. All were of at least average intelligence. The jailer told the prisoners that from three white hats and two red hats he would select three hats and put them on the prisoner's heads. When they were brought together, each was prevented from seeing what color hat was placed on his own head. Except for the blind man, each could see the hats of his fellow prisoners. The jailer offered
freedom to the prisoner with normal vision if he could tell what color hat was on his head. In order to prevent the prisoners from guessing, the jailer told them that the wrong answer would be penalized with death. The prisoner with normal vision said that he could not tell what color hat he was wearing. After hearing the first man's response, the one-eyed prisoner was offered the same deal but he too said that he could not tell what color hat was on his head. The jailer, half-jokingly, offered the same deal to the blind man. The blind prisoner then smiled broadly and said:

"I do not need my sight; from what my friends with eyes have said, I clearly see my hat is ___________.
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Hmm . . . not sure
 
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There doesn't seem to be an answer to this. There is no way the blind man could be sure.

The only way to know is if you know the other two are wearing red hats.

If both the sighted people are wearing red they would each see one red and one white leaving them unable to tell their own colour.

If the blind man was the only one wearing red both sighted people would again see one red and one white.

This means there are two ways the sighted people could not know their colours. One where the blind man i wearing red and one where he is wearing white.

Tis a trick i tells ya
 
Thanks, but none of the responses so far answered the question at hand. The logic problem was an example for the members who might not have known what a logic problem is (I already know the answer to the problem I used).

THE ISSUE: Does anyone have any ideas/advice/methods for quickly and accurately solving logic problems?

Thanks.
 
No but please post more of these. That was fun

Maybe we can come up with a system between us
 
If I'm not mistaking, and this could be since I haven't had a good night sleep in a while, the blind man is wearing a white hat.

As for the question of the thread, I'd say that there are many different logic problems. I think that there is some sort of generalisation but it sure doesn't cover all possible problems. If you are dealing with the problem similar as one you've presented here, I'd say that the quickest way is to see what was the underline idea behind the problem. While reading this one should make a mental note of sorts "three white hats and only two red, there must be a good reason why they gave that". In my opinion the solutions is always in the question itself.
 
Also for the presented problem you could go with truth tables, since you don't have to many combinations, but I didn't go that way. My idea was, if the first one wasn't sure what he had on his head, and the second one also, than that means that they were both seeing one white and one red hat, from which one could draw the conclusion that the hats on their heads were red, and that the hat on the blind man head was white. I don't see a flaw in my reasoning yet, but there is still time. :D
 
Poetic Justice said:
No but please post more of these. That was fun

Maybe we can come up with a system between us
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Okay, sure, that sounds good. This next problem is called 100 Gold Coins, a bit harder than the hats problem. It goes...

100 Gold Coins said:
Five pirates have obtained 100 gold coins and have to divvy up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).

The captain always suggests a distribution of the loot. All pirates vote on his proposal, and if 50% of the crew or more say "Aye", the loot is divvied as proposed, as no pirate would be willing to take on the captain without superior force on their side.

If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.

What is the maximum number of coins the captain can keep without risking his life?
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As a note to other members, if you'd like to participate in answering the logic problems, please refrain from using the Internet to find solutions, as I'm sure most of the ones I have on hand are common on the net.
 
Don't take this in a dismissive way but when stuff like this is posted - my knee jerk reaction is "Ugh, who cares".

I've often wondered if this is common in other INFJs or if this is me just being lazy.

Although, I agree with PJ. The two prisoners with eyesight were wearing ready hats.
 
I find that a lot of NF's struggle with logic. To me, it just doesn't hold much value. My brain is programmed in a much more subjective and philosophical way. Logic really conflicts with that.
 
Sorry but no. I think you are assuming that both red hats have to be worn by someone. It doesn't state that
 
Siamese cat said:
If I'm not mistaking, and this could be since I haven't had a good night sleep in a while, the blind man is wearing a white hat.

As for the question of the thread, I'd say that there are many different logic problems. I think that there is some sort of generalisation but it sure doesn't cover all possible problems. If you are dealing with the problem similar as one you've presented here, I'd say that the quickest way is to see what was the underline idea behind the problem. While reading this one should make a mental note of sorts "three white hats and only two red, there must be a good reason why they gave that". In my opinion the solutions is always in the question itself.
Click to expand...

In most cases, I agree that problems like these have the solutions in them, and perhaps (hindsight being as it is) the example problem I originally chose wasn't the best to use. More or less, I'm looking for quicker methods than drawing out the possibilities, writing out the rules in the problem, things that wouldn't allow one to, in most cases, complete a test in a short time frame with an abundance of these kinds of problems on them.
 
Detective Conan said:
In most cases, I agree that problems like these have the solutions in them, and perhaps (hindsight being as it is) the example problem I originally chose wasn't the best to use. More or less, I'm looking for quicker methods than drawing out the possibilities, writing out the rules in the problem, things that wouldn't allow one to, in most cases, complete a test in a short time frame with an abundance of these kinds of problems on them.
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Yea but practice makes perfect, if you are familiar with the Ainstaine's intelligence test, the one with five houses, five men, five types of cigaretes, five pets and five beers, where in the end you are asked who owns a fish as a pet, if you practice that kind of problems on paper first after several of those you'll be ahead of the logic behind them so much that you can solve them in your head without thinking too much about them or even writing anything on paper.
 
Poetic Justice said:
Sorry but no. I think you are assuming that both red hats have to be worn by someone. It doesn't state that
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starwars.jpg


Use your Ni, PJ. Trust your feeling!
 
I've working on this and still can't find a solution to your question.
 
Wyst said:
Don't take this in a dismissive way but when stuff like this is posted - my knee jerk reaction is "Ugh, who cares".

I've often wondered if this is common in other INFJs or if this is me just being lazy.
Click to expand...

I have that same reaction, Wyst. However, I'm stuck in an obligatory bind to work out problems like these for another few months, hence why I'm looking for some advice/methods early on to prevent a strained knee :).

As RL said, it might be a common trend for INFJs to struggle with these sort of problems in one way or another.

Raccoon Love said:
I find that a lot of NF's struggle with logic. To me, it just doesn't hold much value. My brain is programmed in a much more subjective and philosophical way. Logic really conflicts with that.
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Here I was hoping it was just me, not an NF-wide issue (I'm still hoping it's not, otherwise I don't suspect I'll get a lot of valuable feedback here). I'm already getting a headache trying to solve/justify the second problem I posted here on the thread x_x
 
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