Tips for solving logic problems quickly?

[Poetic Justice]

What makes you say 34, PJ? I got a completely different answer from yours, 98.

Never mind. This doesn't have an answer either

It depends whether his men are willing to take minority share.

I said 34 because i was thinking of splitting it equally between the captain and the two men he needs on his side with one extra for the captain.

Then i thought 48 because i thought well maybe just give them one more than they should get if it's done fairly to placate them leaving 48.

You could argue a case for all sorts of different amounts

Do you know any proper ones?

 

[Detective Conan]

Never mind. This doesn't have an answer either

It depends whether his men are willing to take minority share.

I said 34 because i was thinking of splitting it equally between the captain and the two men he needs on his side with one extra for the captain.

Then i thought 48 because i thought well maybe just give them one more than they should get if it's done fairly to placate them leaving 48.

You could argue a case for all sorts of different amounts

Do you know any proper ones?

Actually, this one did have a proper solution. (I think...... not sure now lol)

Let's give the pirates labels for the sake of making the explanation (at least by how I reached an answer of 98) easier to follow. The Captain is included with the five pirates, but I labeled him with a number as well. I labeled the pirates 1 through 5, with 1 being the most senior pirate and 5 being the lowest-ranking pirate (keep in mind the problem says the pirates have a chain of command toward the end there).

Let's say 5 proposes to take ninety-eight of the gold coins and give one coin to 1 and one coin to 3. Granted, this proposal wouldn't be easily accepted, so 5 needs to persuade pirates to 1-4 to give him at least a 50% vote (I found role-playing here helped me a lot). 1 goes about to explain why his plan should be voted for:

If there were only two pirates, with 2 being the captain, then 2 would vote to keep all the money because he meets the 50% vote.

If there were three pirates, with 3 being the captain, 3 needs to convince either 1 or 2 to join his vote. Pirate 3 proposes a similar plan as the one that currently stands, except pirate 3 keeps ninety-nine coins and gives one coin to 1. 1 must vote with 3, or else not get anything, as the problem from the above paragraph would arise with only two pirates present.

If there were four pirates, with 4 being the captain, 4 would give 2 a coin to vote for his plan, and since 2 wouldn't get anything (look to the original paragraph for the problem) if he didn't vote with 4, then he votes for 4's plan.

Now, to the current situation with five pirates, 1 and 3 should vote for 5's plan, or else they won't get any coins or risk facing death.



Sorry it took so long to type that; using numbers as labels didn't make things any easier on my end for explaining why the above solution works.

EDIT: I'll find another problem and type it up later. Some of the problems here in this book require pictures, so I'm sifting through which ones don't require any drawing whatsoever to explain.

[MENTION=1669]Anita[/MENTION]: could you explain the scheme for how you arranged the table? It's not making much sense to me, but then again, I just crapped my brain out with that 100 gold coins problem.

 

[Gaze]

*methinks i will weird someone out with my table*

 

[Bird]

Google.

 

[Detective Conan]

Google.

Good for tinkering with homework and at home, completely useless while in class during a test ^^; Tempting as it might be, I think it'd be better to learn how to do the problems myself... but that could just be me XD

 

[Poetic Justice]

Hmmm. I'm not convinced about the 100 coins answer.

The captain can't know who the next in line would offer the coins to so he wouldn't an ableTm convince them they'd get nothing if they didn't vote for him.

I could be wrong though. Is that the official answer?

Btw i an also confused by your table anita

 

[Gaze]

Hey, i tried . . .

I think i'm gonna let this logic puzzle rest . . .

Not good at logic puzzles but i figured i'd try anyway.

In the end, what Siamese Cat says makes sense.

 

[Detective Conan]

Hmmm. I'm not convinced about the 100 coins answer.

The captain can't know who the next in line would offer the coins to so he wouldn't an ableTm convince them they'd get nothing if they didn't vote for him.

I could be wrong though. Is that the official answer?

According to the solution manual, 98 is the correct answer with similar reasoning (they just worded what I said differently and offered a little more explanation). You need to keep in mind that all the pirates are extremely intelligent, treacherous, and selfish, too. From that, I figured it would be very likely that the sequence of events that I laid out would be the events to occur with the respective number of pirates.

 

[enfp can be shy]

Well, Solution (to the 1st problem) :

Spoiler

the third man can't have red hat -> so he has white hat; easy as pie
if he had red hat,
- the first one eliminated the case of 2 reds
- the second one can't be seeing 2 reds either, so he would see the red and a white, and realize since the first didn't see 2 reds, he must be white

More interesting note:

Spoiler

on a very fast test which rewards a bit of a risk-taking over accuracy, because you can't answer all questions - you gain from gambling a bit with just your sense. In this case from the very beginning of the setting there are 3 whites 2 reds, so - a good heuristic is to assume the answer is probably white, hence not red.

Setting good heuristics will improve your searching speeds in some cases. Or just allow you to gamble when the clock presses hard.

Overall, there's no recipe for speed, other than - solve a lot of problems. Don't read general guidelines; solve problems. Get a book (which has answers!!) with hundreds of problems; set some daily goal and keep solving every day, eg: ~10 problems, ~20 problems etc. Eventually your brain will develop patterns to help you recognize and solve faster. No one is born with that, it comes with practice. Good luck!

edit:
Ooops, missed the 100 coin problem over 5 pirates. Let's see:

Spoiler

1-100
2-100,0
3-99,0,1
4-99,0,1,0
5-98,0,1,0,1

(leftmost = highest rank)

So: 98

i think this one's easier

p.s. Another note - it helps you after some experience to start thinking about your own problems. How to create a good problem. Put yourself "on the other side". Think through the mind of the task-giver. You will find so many hints intuitively about what's going on in a problem description, that your speed will sky-rocket at this point.

 

[Gaze]

It depends whether his men are willing to take minority share.

That's pretty much one of the few conclusions I could come up with came to when I read the riddle.

 

[Poetic Justice]

Enfp can be shy, what if the blind man is the only one wearing red? Person 1 would see red and white which means he wouldn't know what his was. Person 2 would also see red and white so wouldn't know either.

 

[Poetic Justice]

Never mind. I get it.

You're right it's white.

I wish i could edit my posts. Stupid phone

 

[Gaze]

p.s. Another note - it helps you after some experience to start thinking about your own problems. How to create a good problem. Put yourself "on the other side". Think through the mind of the task-giver. You will find so many hints intuitively about what's going on in a problem description, that your speed will sky-rocket at this point.

Agree. There seems to be a narrow frame of reference given for solving logical puzzles. You're expected to go through all possibilities or probabilities to get to the "truth." But they're usually other methods but not as acceptable as the typical ones for solving them.