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Math game...

If you ask the first 2 questions to the same person, and that person is the random answer guy, nothing has been learned. His answers are completely random.

Unless you get lucky, and he reveals his random nature. Then it is simple to figure out who the other 2 are with one question.
 
Michael74 said:
If you ask the first 2 questions to the same person, and that person is the random answer guy, nothing has been learned. His answers are completely random.
Click to expand...

Not if you ask the right questions. If you ask a question to which you know the answer, such as "am I waring a baseball cap" then, If he answers correctly ("yes", if you are wearing a baseball cap), then you know that he's not the one who always lies, but if he answers incorrectly ("no" if you are wearing a baseball cap), you know he's not the one who always tells the truth. You've already ruled out one possibility with the first question, no matter what the answer is. Then you just have to devise a second question that will tell you which of the two he is.

The TOG​
 
Yes, but no matter what the 2nd question is, random has a 50/50 chance of answering it the same as the other guy would.

Eventually random would reveal his nature with consecutive questions, but 2 consecutive questions to random would only give you a probability, not a certainty. Randomly generated sequences contain long strings of yeses and nos. They don't alternate yes and no regularly. That's why password generators use pseudo random number generators, rather than true random number generators. The puzzle setup specified a random answer generator.
 
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Michael74 said:
Yes, but no matter what the 2nd question is, random has a 50/50 chance of answering it the same as the other guy would.
Click to expand...

Not if you ask the right question. Like I pointed out earlier, the second question has multiple parts, so that all have to be true for the whole question to be true. By carefully selecting the different parts of the question, you can make it so that the one who answers randomly will give the same answer, whether he is lying or telling the truth, and the other possible one, whether it is the one who always lies or always tells the truth, will give a different answer.

The TOG​
 
Mary wants to make a box. She starts with a piece of cardboard whose length is 15 centimeters and with is 10 centimeters. Then she cuts congruent squares with side of 3 centimeters at the four corners. What is the area of the cardboard after she cuts the 4 corners?
problem_2.gif
Ok all you math wizards.Solve this :)
 
TOG said:
No, my solution doesn't include the non-English responses. It may help people get on the right track though. Since agua. was trying to figure it out, I'll wait till he responds before I give the answer. It still took quite a while to figure out, even with English answers.

The TOG​
Click to expand...

Go ahead TOG show us the money mate it'll probably take me another week if I get it at all :D
 
Kathi said:
Mary wants to make a box. She starts with a piece of cardboard whose length is 15 centimeters and with is 10 centimeters. Then she cuts congruent squares with side of 3 centimeters at the four corners. What is the area of the cardboard after she cuts the 4 corners?
problem_2.gif
Ok all you math wizards.Solve this :)
Click to expand...

Including the cut off bits or not ? :D
 
Kathi said:
Mary wants to make a box. She starts with a piece of cardboard whose length is 15 centimeters and with is 10 centimeters. Then she cuts congruent squares with side of 3 centimeters at the four corners. What is the area of the cardboard after she cuts the 4 corners?
problem_2.gif
Ok all you math wizards.Solve this :)
Click to expand...

Well... There are a few ways of figuring this out. For example, you could calculate the little rectangles along the edges and then add the big one in the middle.

(2*((10-3-3)*3)) + (2*((15-3-3)*3)) + ((10-3-3) * (15-3-3))

Or you could take the small rectangles along the ends separately and look at the rest as one big rectangle.

(2*((10-3-3)*3) + ((15-3-3)*10)

Or you could take the long rectangles along the edges separately and look at the rest as one big rectangle.

(2*((15-3-3)*3) + ((10-3-3)* 15)

Or you could just subtract the small squares from the big rectangle.

(10*15) - (4*3*3)

However you do it, it comes out 114 cm²

The TOG​
 
TOG said:
Well... There are a few ways of figuring this out. For example, you could calculate the little rectangles along the edges and then add the big one in the middle.

(2*((10-3-3)*3)) + (2*((15-3-3)*3)) + ((10-3-3) * (15-3-3))

Or you could take the small rectangles along the ends separately and look at the rest as one big rectangle.

(2*((10-3-3)*3) + ((15-3-3)*10)

Or you could take the long rectangles along the edges separately and look at the rest as one big rectangle.

(2*((15-3-3)*3) + ((10-3-3)* 15)

Or you could just subtract the small squares from the big rectangle.

(10*15) - (4*3*3)

However you do it, it comes out 114 cm²

The TOG​
Click to expand...
Yes :)
 
agua. said:
Go ahead TOG show us the money mate it'll probably take me another week if I get it at all :biggrin
Click to expand...

Call the men Andy, Bill and Carl.
They can...
Always answer truthfully (T)
Always answer falsely (F)
Answer randomly (R)

R can either

Answer truthfully (RT) or
Answer falsely (RF)

Assume you are wearing a baseball cap.

1. Ask Andy "Am I wearing a baseball cap?"
If he answers "yes", then he is either T or RT.
If he answers "no", then he is either F or RF.

If Andy answered "yes" to question 1, then.

2a. Ask Andy "Is exactly one of the following statements true?
a. You are the one who always tells the truth.
b. I am wearing a baseball cap.
c. You are lying."​

If Andy = T, then the correct answer is "no" (both a. and b are true) and he will answer truthfully and say "no".
If Andy = RT, then the correct answer would be "yes" (only b. is true) and he will answer truthfully and say "yes".
If Andy = RF, then the correct answer would be "no" (both b. and c. are true), but he would lie and say "yes".

If Andy answered "no" to question 1, then

2b. Ask Andy "Is exactly one of these statements true?
a. You are the one who always lies.
b. I am wearing a baseball cap.
c. You are telling the truth.
​
If Andy = F, then the correct answer is "no" (both a. and b are true) but he will lie and say "yes".
If Andy = RT, then the correct answer would be "no" (both b. and c. are true) and he will answer truthfully and say "no".
If Andy = RF, then the correct answer would be "yes" (only b. is true), but he would lie and say "no".

If Andy answered "yes" to question 1 and "yes" to question 2a, then he is the one who answers randomly.

3a. Ask Bill "Am I wearing a baseball cap?"

If Bill = T, then he will answer truthfully and say "yes".
If Bill = F, then he will lie and say "no".

If Andy answers "yes" to question 1 and "no" to question 2a, then he is the one who always tells the truth.

3b. Ask Andy "Is Bill the one who always lies?"

If Bill = F, then Andy will answer truthfully and say "yes".
If Bill = R then Andy will answer truthfully and say "no"

If Andy answers "no" to question 1 and "yes" to question 2b ,then he is the one who always lies.

3c. Ask Andy "Is Bill the one who always tells the truth?"

If Bill = T, then Andy will lie and say "no".
If Bill = R, then Andy will lie and say "yes".

If Andy answered "no" to question 1 and "no" to question 2b, then he is the one who answers randomly.

3d. Ask Bill "Am I wearing a baseball cap?"

If Bill = T, then he will answer truthfully and say "yes".
If Bill = F, then he will lie and say "no".

4. Ask yourself "Am I confused yet? "

If you answered question 4 "no", then congratulations are in order. Keep going.
If you answered question 4 "yes", then go get a strong dose of caffeine or other stimulant to keep you alive through the rest of this post, and a couple of aspirins for later.

Here are the results...

Question 1 - YES
Question 2a - YES
Question 3a - YES
Andy = R
Bill = T
Carl = F

Question 1 - YES
Question 2a - YES
Question 3a - NO
Andy = R
Bill = F
Carl = T

Question 1 - YES
Question 2a - NO
Question 3 - YES
Andy = T
Bill = F
Carl = R

Question 1 - YES
Question 2a - NO
Question 3b - NO
Andy = T
Bill = R
Carl = F

Question 1 - NO
Question 2b - YES
Question 3c - YES
Andy = F
Bill = R
Carl = T

Question 1 - NO
Question 2b - YES
Question 3c - NO
Andy = F
Bill = T
Carl = R

Question 1 - NO
Question 2b - NO
Question 3d - YES
Andy = R
Bill = T
Carl = F

Question 1 - NO
Question 2b - NO
Question 3d - NO
Andy = R
Bill = F
Carl = T

Congratulations for making it to the end. Have some more caffeine. :pepsi2

The TOG​
 
Interesting. The 3 statement question is posited a way to trick sometimes liars into simultaneously answering 3 questions (framed as statements) truthfully, in order to lie about the leading question.

I don't think it would work in real life. Otherwise the justice system would use such compound statements to infallibly elicit the truth, and no expensive trials would be needed. Sometimes liars are not generally silly enough to be tricked by such ruses. They would lie about the 3 statements individually, as well as the leading question.

However, you can take to prize on this puzzle. Congratulations on your ingenuity.
 
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TOG said:
Call the men Andy, Bill and Carl.
They can...
Always answer truthfully (T)
Always answer falsely (F)
Answer randomly (R)

R can either

Answer truthfully (RT) or
Answer falsely (RF)

Assume you are wearing a baseball cap.

1. Ask Andy "Am I wearing a baseball cap?"
If he answers "yes", then he is either T or RT.
If he answers "no", then he is either F or RF.

If Andy answered "yes" to question 1, then.

2a. Ask Andy "Is exactly one of the following statements true?
a. You are the one who always tells the truth.
b. I am wearing a baseball cap.
c. You are lying."​

If Andy = T, then the correct answer is "no" (both a. and b are true) and he will answer truthfully and say "no".
If Andy = RT, then the correct answer would be "yes" (only b. is true) and he will answer truthfully and say "yes".
If Andy = RF, then the correct answer would be "no" (both b. and c. are true), but he would lie and say "yes".

If Andy answered "no" to question 1, then

2b. Ask Andy "Is exactly one of these statements true?
a. You are the one who always lies.
b. I am wearing a baseball cap.
c. You are telling the truth.
​
If Andy = F, then the correct answer is "no" (both a. and b are true) but he will lie and say "yes".
If Andy = RT, then the correct answer would be "no" (both b. and c. are true) and he will answer truthfully and say "no".
If Andy = RF, then the correct answer would be "yes" (only b. is true), but he would lie and say "no".

If Andy answered "yes" to question 1 and "yes" to question 2a, then he is the one who answers randomly.

3a. Ask Bill "Am I wearing a baseball cap?"

If Bill = T, then he will answer truthfully and say "yes".
If Bill = F, then he will lie and say "no".

If Andy answers "yes" to question 1 and "no" to question 2a, then he is the one who always tells the truth.

3b. Ask Andy "Is Bill the one who always lies?"

If Bill = F, then Andy will answer truthfully and say "yes".
If Bill = R then Andy will answer truthfully and say "no"

If Andy answers "no" to question 1 and "yes" to question 2b ,then he is the one who always lies.

3c. Ask Andy "Is Bill the one who always tells the truth?"

If Bill = T, then Andy will lie and say "no".
If Bill = R, then Andy will lie and say "yes".

If Andy answered "no" to question 1 and "no" to question 2b, then he is the one who answers randomly.

3d. Ask Bill "Am I wearing a baseball cap?"

If Bill = T, then he will answer truthfully and say "yes".
If Bill = F, then he will lie and say "no".

4. Ask yourself "Am I confused yet? "

If you answered question 4 "no", then congratulations are in order. Keep going.
If you answered question 4 "yes", then go get a strong dose of caffeine or other stimulant to keep you alive through the rest of this post, and a couple of aspirins for later.

Here are the results...

Question 1 - YES
Question 2a - YES
Question 3a - YES
Andy = R
Bill = T
Carl = F

Question 1 - YES
Question 2a - YES
Question 3a - NO
Andy = R
Bill = F
Carl = T

Question 1 - YES
Question 2a - NO
Question 3 - YES
Andy = T
Bill = F
Carl = R

Question 1 - YES
Question 2a - NO
Question 3b - NO
Andy = T
Bill = R
Carl = F

Question 1 - NO
Question 2b - YES
Question 3c - YES
Andy = F
Bill = R
Carl = T

Question 1 - NO
Question 2b - YES
Question 3c - NO
Andy = F
Bill = T
Carl = R

Question 1 - NO
Question 2b - NO
Question 3d - YES
Andy = R
Bill = T
Carl = F

Question 1 - NO
Question 2b - NO
Question 3d - NO
Andy = R
Bill = F
Carl = T

Congratulations for making it to the end. Have some more caffeine. :pepsi2

The TOG​
Click to expand...

Hmm isn't asking a 3 question question 3 questions ? :D Sorry TOG couldn't resist.

Well done mate impressive stuff.

roasted-chicken-dinner.jpg

http://theheritagecook.com/wp-content/uploads/2010/05/roasted-chicken-dinner.jpg
 
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Michael74 said:
Interesting. The 3 statement question is posited a way to trick sometimes liars into simultaneously answering 3 questions (framed as statements) truthfully, in order to lie about the leading question.

I don't think it would work in real life. Otherwise the justice system would use such compound statements to infallibly elicit the truth, and no expensive trials would be needed. Sometimes liars are not generally silly enough to be tricked by such ruses. They would lie about the 3 statements individually, as well as the leading question.

However, you can take to prize on this puzzle. Congratulations on your ingenuity.
Click to expand...

No, it probably wouldn't work in real life, but that's because it isn't real life; it's a logic puzzle. Nobody in real life actual always lies or always tells the truth. That's only in logic puzzles.

The TOG​
 
Here's an easy one for you...

Maggies mom has 5 daughters...

Jani
Jeni
Jini
Joni

What is the name of the 5th daughter?

The TOG​
 
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