If you are more logical than I am, please explain this to me.

[Biggirl]

This is one of those blog quizzes called How Logical Are You?

Firstly, I got 75% right. I don't know which ones because the little quiz doesn't tell you. I'm sure I did not get this one right:

5. Your room is completely dark. You have eight shoes of four different colors, and fifty socks of five different colors. How many shoes and socks must you grab to make sure you have a matching pair?

5 shoes, 6 socks
6 shoes, 8 socks
6 shoes, 10 socks
5 shoes, 5 socks



How do you figure this out?

[rjk]

Start picking shoes. The first certainly doesn't make a pair. Take another - could still be different. Another - the same. And the fourth. But you've run out of colours, so the fifth must match one of the others you've taken,

Socks work the same, except five colours make you take six to force a pair.

[CandidGamera]

Assuming you can feel the shoes well enough to tell if they're right or left foot, and assuming socks that aren't foot specific, It's 5 and 6, I think.

Why? Well, take them individually. You have eight shoes of four colors - presumably, four matched pairs of shoes. Grab all four left shoes and one right shoe, and bam! You're guaranteed to have one of your matched pairs.

The socks are more complex - 50 socks, 25 pairs, with 5 pairs in each of five colors. So, five pairs of red, five pairs of blue, etc. But essentially, the number of colors is what matters - If you took five, you could theoretically have one of each color; but if you take six, you have to repeat a color, and thus have a matched pair.

[klintypooh]

I think you need to grab 5 shoes and 6 socks.

I worked it out as......... If you grab 4 shoes you may get one of each colour but whatever shoe you grab next you will definately have a pair.
Same for the different coloured socks, you can grab 5 different coloured socks so the 6th must match 1 of them.

Although just because socks are the same colour, doesn't mean they match but that seems to be just bad wording.



I think.

[Biggirl]

Originally Posted by CandidGamera

Assuming you can feel the shoes well enough to tell if they're right or left foot, and assuming socks that aren't foot specific, It's 5 and 6, I think.

Ah! This is where I screwed up. I'm thinking "I'd have to grab at least 9 shoes to make sure I've got a left and a right but that's not one of the choices."

[rjk]

Yes, CandidGamera noticed the left-right difficulty I missed with the shoes, but if you think about it you don't need to care - the two colour-matched shoes MUST be l-r. Socks, on the other hand, don't need l-r anyway, and mine at least are all the same style if they're the same colour.

[Cinnamon Girl]

Answers in spoiler:

1. Ralph is four times as old as Frank. In 20 years, Ralph will be twice as old as Frank. How old are Ralph and Frank?

• Ralph is 40; Frank is 10.
• Ralph is 20; Frank is 5.
• Ralph is 60; Frank is 15.
• Ralph is 80; Frank is 20.

SPOILER:

Ralph is 40; Frank is 10.

2. If Jenny hits a home run, her team will win. Given that this is true, what else also must be true?

• If the team won, Jenny hit a home run.
• If Jenny didn't hit a home run, the team tied.
• If the team didn't win, Jenny didn't hit a home run.
• All of the above.

SPOILER:

If the team didn't win, Jenny didn't hit a home run.

3. Taking the below statements as a group, which statement is the true one?

• The number of false statements here is one.
• The number of false statements here is two.
• The number of false statements here is three.
• The number of false statements here is four.

SPOILER:

The number of false statements here is three.

4. Neko will go to the movies, only if she can drive. Given that this is true, what else also must be true?

• If Neko didn't drive, she didn't go to the movies.
• If Neko went to the movies, then she drove.
• Both of the above statements.
• If Neko drove, then she went to the movies.

SPOILER:

Both of the above statements.

5. Your room is completely dark. You have eight shoes of four different colors, and fifty socks of five different colors. How many shoes and socks must you grab to make sure you have a matching pair?

• 5 shoes, 6 socks
• 6 shoes, 8 socks
• 6 shoes, 10 socks
• 5 shoes, 5 socks

SPOILER:

5 shoes, 6 socks

6. No musicians are chefs. No chefs are teachers. Given that these are true, what else also must be true?

• No teacher is a musician.
• Some musicians are teachers.
• Some teachers are chefs.
• None of the above.

SPOILER:

None of the above.

7. If QUIZ is written as UYMD, how do you write HEAD?

• MIEH
• MJEH
• LJEH
• LIEH

SPOILER:

LIEH

8. Some tigers are not lions. All lions are mammals. Given that these are true, what else also must be true?

• Some tigers are lions.
• Some mammals are not lions.
• Some lions are not tigers.
• None of these

SPOILER:

None of these

What I'd like to know is how lavendar underwear make me a Flu Phlegm Green Crayola?

[AHunter3]

The socks are more complex - 50 socks, 25 pairs, with 5 pairs in each of five colors.

To be sure, they didn't say the 50 socks that come in five colors consist of 5 pairs each. For all we know, the fifty socks could consist of three white socks, five green socks, one red sock, three black socks, and 38 blue socks. You're still good if you fetch six socks at random. At least two of them will match.

I missed the driving-to-the-movies question because I saw a right answer and didn't realize the next answer was also correct followed by a "both of the above"; missed the chef/musician/teacher one for absolutely no good reason

[Excalibre]

Originally Posted by AHunter3

To be sure, they didn't say the 50 socks that come in five colors consist of 5 pairs each. For all we know, the fifty socks could consist of three white socks, five green socks, one red sock, three black socks, and 38 blue socks. You're still good if you fetch six socks at random. At least two of them will match.

Yeah, but who says the shoes and socks will then match? And will they match your pants? Are the pants that go with the blue socks clean? Maybe you should fold your socks and turn the lights on when you pick them.

[cromulent]

I don't get the lion/tiger one. The statement

"Some tigers are not lions"

basically implies that some tigers are lions. It doesn't literally say that, but if I say "some days I feel tired," you can be pretty sure that some days, I don't.

[audiobottle]

I missed question 6. That makes me 88% logical. According to this site, my brain is like a computer. I don't think this necessarily follows.
cromulent, you can only assume what is explicitly said.

[Munch]

I don't understand why #8 isn't "Some mammals are not lions." Doesn't "Some tigers are not lions" suggest that "some tigers are lions"? And if all lions are mammals, then "all mammals" must certainly contain "some tigers which are lions - which are therefore mammals". No?

[Munch]

Originally Posted by audiobottle

I missed question 6. That makes me 88% logical. According to this site, my brain is like a computer. I don't think this necessarily follows.
cromulent, you can only assume what is explicitly said.

Yes, but I have the following diagram:

              ________                                 
             /   M    \                               
            /      ___ \                               
            |     / L \|                              
            |     |   ||                              
            \     \___//                              
             \________/

The circle for tigers would either be completely enclosed by Mammals, or go outside of Mammals - but some part of it would be inside of it at all times, would it not?

[Munch]

To clarify, the Tiger circle would intersect the Lion circle ("not all Lions are Tigers") - all of which is inside the Mammal circle ("all Lions are Mammals").

[Kamino Neko]

Some can be All. It just doesn't have to be.

Some tigers are not lions.
All lions are mammals.

Nothing is said about the portion of the tiger set that haven't been sampled, or the mammal set that isn't lions.

[iampunha]

Originally Posted by Munch

I don't understand why #8 isn't "Some mammals are not lions." Doesn't "Some tigers are not lions" suggest that "some tigers are lions"?

Not necessarily. For example, I have fifteen coins. [at least]* Some of them are not nickels. Are any of the others required to be nickels?

I think the question is worded improperly, FWIW. It requires you to think about what logical argument the question writer is trying to use, rather than just thinking about the logic of the problem itself. "What was the question writer thinking at the time" is an incredibly annoying way to have to think.

*This was not part of the verbatim wording of the question, but I thought when I answered the question that it's what the question writer was thinking about. I got it right only because of that.