BRAIN TEASERS THREAD [Archive] - Two Plus Two Newer Archives

ScottySo

10-19-2006, 08:10 PM

here are 2 decent ones to get started.

RIDDLE NUMBER - DIFFICULTY RATING 3/10

a king has 10 tax-collectors, who each month bring him 10 coins each, and each coin weighs 10 ounces. every month the king uses his magic scale, which can only make one reading per month, to make sure all 1,000 ounces of coins are there. one month, a spy comes to him and tells him one of his collectors is shaving an ounce of each coin. he wants to find out who it is this month, so using one weighing only, how does the king determine which collector is the cheat?

RIDDLE #2 - DIFFICULTY RATING 8.5/10

You have 12 coins, 11 weigh the exact same amount but one (you don't know which) is of a different weight (you also don't know whether its heaver or lighter. you have a scale, using 3 weighings figure out which coin is the odd one and whether it is heavier or lighter.

ScottHoward

10-19-2006, 08:27 PM

you guys know theres a puzzle and other games forum?
might get better action in there

Utah

10-19-2006, 09:30 PM

I have done the second one before and it is one of my favorite puzzles. Since I have done it before, there is no reason to post the answer.

However, I believe I have the first 1. Sadly, it took almost 30 minutes to figure out because I am an idiot.

Answer in white:

Left side of scale:
Collector 1: 1 coin
Collector 2: 2 coin
Collector 3: 3 coin
Collector 4: 4 coin
Collector 5: 5 coin
Collector 6: 6 coin
Collector 7: 7 coin
Collector 8: 8 coin
Collector 9: 9 coin
Collector 10: 10 coin

Right side of scale: Use 10 ounce and 1 once units. I can tell who the cheat is by how many 1 ounce units I use.

Borodog

10-19-2006, 09:43 PM

What is the simplest possible family tree?

1. ACGTCTTCCGCGAGCCGCATATAGCGCTAGCTAGACGCT
2. ACGTCGACCGCCAGCCGCATATAGCGCTCGCTAGACGCT
3. ACGTCTACCGCTAGCCGCATTTAGCGCTACCTAGACGCT
4. ACGTCTAGCGCTAGCCGCATATGGCGCTCGCTAGTAGCT
5. ACGACGACCGCTAGCCGCATATAGCGATCGCTAGACGCT
6. ACGTCTAGCGCTAGCCGCTTATTGCGCTCGCTAGAAGCT
7. ACGTCTACCGCGAGCCGCATATAGCGCTAGCTGGACGCT
8. ACGTCTAGCGCTAGCCGCTTATTGCGCTCGCTAGATGCT
9. ACGTCTACCGCTAGCCGCATATAGCGCTACCTAGACGCA

FortunaMaximus

10-19-2006, 10:01 PM

4.?

Looks like she's from Tennessee anyway.

Borodog

10-19-2006, 11:06 PM

I believe the correct answer is :

{(2,5),[(1,7),(3,9)]},[(6,8),4]

FortunaMaximus

10-19-2006, 11:29 PM

Weird. Anyway.

Magic_Man

10-19-2006, 11:32 PM

It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

FortunaMaximus

10-19-2006, 11:43 PM

With what, half a shovel? /images/graemlins/tongue.gif

DCopper04

10-20-2006, 12:26 AM

[ QUOTE ]
It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

[/ QUOTE ]

Answer: 40/13 days?

Magic_Man

10-20-2006, 01:24 AM

One of my favorites from long ago, I hope I get it right. I have purposefully changed the usual wording to prevent easy googling:

A & B are integers greater than 1 and less than 100.

Mr. Add knows (A+B)
Mr. Multiply knows (A*B)

Mr. Add says to Mr. Multiply, "You don't know A and B."
Mr. Multiply says, "Now I do know A and B."
Mr. Add says, "Now I do too."

What are A & B?

~MagicMan

Eihli

10-20-2006, 05:52 AM

According to the late philosopher and logician George Boolos, who was a professor at MIT, the hardest logical puzzle is one that was invented by the logician and puzzle-master Raymond Smullyan, and modified slightly by the computer scientist John McCarthy. Here is the puzzle :

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

This was posted in OOT years back. I have held off looking up the answer.

Winenose

10-20-2006, 06:28 AM

This looks interesting..

I assume that first saying means that A*B has at least two sets of A and B that can make it.

First number like this is 12. It can be found by 2x6 and 3x4. Next is 16, then 18, then 20, 24, 28, 30, etc..

And that's where my ideas run out.

ScottHoward

10-20-2006, 11:14 AM

[ QUOTE ]
It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

[/ QUOTE ]
wtf is half a hole?

Borodog

10-20-2006, 02:42 PM

[ QUOTE ]
[ QUOTE ]
It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

[/ QUOTE ]
wtf is half a hole?

[/ QUOTE ]

Hence the correct answer is an infinite amount of time, since you can never dig half a hole.

Drunken Monkey

10-20-2006, 03:11 PM

[ QUOTE ]

RIDDLE #2 - DIFFICULTY RATING 8.5/10

You have 12 coins, 11 weigh the exact same amount but one (you don't know which) is of a different weight (you also don't know whether its heaver or lighter. you have a scale, using 3 weighings figure out which coin is the odd one and whether it is heavier or lighter.

[/ QUOTE ]

Is this a scale where you put a coin on it and it gives you a numerical weight of that coin? Or is it a scale where you compare two items by placing them in different plates and watching which way the bar is tipped (a balance scale)? I am assuming the latter, but I just wanted to be clear.

Also, where did you get this rating system?

ScottySo

10-20-2006, 03:29 PM

in riddle #1 you have a bathroom scale, i.e. you put your coins on it and it gives you the weight. in the second one is a balance scale to compare weights. the guy on the first page got it right.

valenzuela

10-20-2006, 04:51 PM

We have 3 cannibals and 3 explorers and a boat that has the capacity for 2 ppl. How do you pass all 6 persons safely from one side fo the river to the other of the river?
If there is ever more cannibals than explorers on either side the cannibals will eat the explorers.

metsandfinsfan

10-20-2006, 05:27 PM

again guys if you post these in pog you will get more responses

although i think we have seen most of these already

metsandfinsfan

10-20-2006, 05:31 PM

here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

amirite

10-20-2006, 05:34 PM

[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

lol alphandralphaments

random

10-20-2006, 05:39 PM

Take a cannibal and explorer over first. Take the canibal back. Drop him off, grab the other two explorers.

metsandfinsfan

10-20-2006, 05:50 PM

[ QUOTE ]

lol alphandralphaments

[/ QUOTE ]

I have absolutely no idea what that means

Magic_Man

10-20-2006, 07:20 PM

How about "lol davidbowieaments (http://www.imdb.com/title/tt0091369/)" instead then?

~MagicMan

gumpzilla

10-20-2006, 11:37 PM

[ QUOTE ]

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Good one: Which way would your brother tell me the hospital is if I asked him? The truthful one knows his brother will tell you the wrong way, and thus will point the wrong way. The deceitful one knows his brother will tell you the right way, so will point the wrong way. So go whichever way they don't point.

CORed

10-21-2006, 01:28 PM

[ QUOTE ]
It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

[/ QUOTE ]

It takes one woman 9 months to have a baby. How long does it take 9 women?

hmkpoker

10-21-2006, 05:07 PM

[ QUOTE ]
What is the simplest possible family tree?

1. ACGTCTTCCGCGAGCCGCATATAGCGCTAGCTAGACGCT
2. ACGTCGACCGCCAGCCGCATATAGCGCTCGCTAGACGCT
3. ACGTCTACCGCTAGCCGCATTTAGCGCTACCTAGACGCT
4. ACGTCTAGCGCTAGCCGCATATGGCGCTCGCTAGTAGCT
5. ACGACGACCGCTAGCCGCATATAGCGATCGCTAGACGCT
6. ACGTCTAGCGCTAGCCGCTTATTGCGCTCGCTAGAAGCT
7. ACGTCTACCGCGAGCCGCATATAGCGCTAGCTGGACGCT
8. ACGTCTAGCGCTAGCCGCTTATTGCGCTCGCTAGATGCT
9. ACGTCTACCGCTAGCCGCATATAGCGCTACCTAGACGCA

[/ QUOTE ]

What makes a family tree "simple"? I don't understand the question.

metsandfinsfan

10-21-2006, 05:07 PM

gump i dont know if you worded it right, but yes you got the answer

hmkpoker

10-21-2006, 06:57 PM

rjohson

10-21-2006, 08:24 PM

it all depends if he has a half of brain or not

rjohson

10-21-2006, 08:32 PM

there was this man who had with him a chicken, a fox, and some chicken feed. he needed to get to the other side of the river, but he boat he had was not big enough to take him, the chicken, the feed, and the fox all on one trip. he could only take one of the three. his problem was that if he took the fox across, and left the chicken and feed behind, the chicken would eat the feed, if he took the feed, and left the fox and chicken behind, the fox would eat the chicken. your mission is, if you choose to accept it, find a way for the man to get across the river with all three items.

Deorum

10-21-2006, 09:20 PM

[ QUOTE ]
One of my favorites from long ago, I hope I get it right. I have purposefully changed the usual wording to prevent easy googling:

A & B are integers greater than 1 and less than 100.

Mr. Add knows (A+B)
Mr. Multiply knows (A*B)

Mr. Add says to Mr. Multiply, "You don't know A and B."
Mr. Multiply says, "Now I do know A and B."
Mr. Add says, "Now I do too."

What are A & B?

~MagicMan

[/ QUOTE ]

Okay, no matter what I try I keep getting a dead end on this one. What is the answer?

Deorum

10-21-2006, 09:24 PM

[ QUOTE ]
there was this man who had with him a chicken, a fox, and some chicken feed. he needed to get to the other side of the river, but he boat he had was not big enough to take him, the chicken, the feed, and the fox all on one trip. he could only take one of the three. his problem was that if he took the fox across, and left the chicken and feed behind, the chicken would eat the feed, if he took the feed, and left the fox and chicken behind, the fox would eat the chicken. your mission is, if you choose to accept it, find a way for the man to get across the river with all three items.

[/ QUOTE ]

Take the chicken, come back, take the feed, come back with the chicken, drop the chicken off and take the fox, come back, take the chicken.

LuckOfTheDraw

10-21-2006, 09:33 PM

I heard this here on 2+2 years ago. It's probably my favorite riddle. Please correct me if I make a mistake in presentation.

Three logicians, who each use perfect logic, have a number written on their foreheads. None of them know what their own number is and are not allowed to tell eachother (obviously). They do know that each number is unique integer and that the sum of the lesser two equals the third. They stand in a circle and look at eachother's numbers. After a couple seconds of thought, one of the logicians asks the others if they know what their numbers are. After they say that they do not know, he announces, "My number is 50."

What are the numbers on the other 2 logicians' foreheads.

iversonian

10-22-2006, 02:00 AM

[ QUOTE ]
there was this man who had with him a chicken, a fox, and some chicken feed. he needed to get to the other side of the river, but he boat he had was not big enough to take him, the chicken, the feed, and the fox all on one trip. he could only take one of the three. his problem was that if he took the fox across, and left the chicken and feed behind, the chicken would eat the feed, if he took the feed, and left the fox and chicken behind, the fox would eat the chicken. your mission is, if you choose to accept it, find a way for the man to get across the river with all three items.

[/ QUOTE ]

YouTube version (http://youtube.com/watch?v=DDzTyOJSe-Y)

metsandfinsfan

10-22-2006, 05:02 AM

LuckOfTheDraw

10-22-2006, 08:47 AM

[ QUOTE ]
[ QUOTE ]
I heard this here on 2+2 years ago. It's probably my favorite riddle. Please correct me if I make a mistake in presentation.

Three logicians, who each use perfect logic, have a number written on their foreheads. None of them know what their own number is and are not allowed to tell eachother (obviously). They do know that each number is unique integer and that the sum of the lesser two equals the third. They stand in a circle and look at eachother's numbers. After a couple seconds of thought, one of the logicians asks the others if they know what their numbers are. After they say that they do not know, he announces, "My number is 50."

What are the numbers on the other 2 logicians' foreheads.

[/ QUOTE ]

is there a min or max for the numbers??? Such as 1-100 and are negatives allowed?

[/ QUOTE ]

no

I should have said unique positive integer.

Winenose

10-22-2006, 09:30 AM

[ QUOTE ]
I heard this here on 2+2 years ago. It's probably my favorite riddle. Please correct me if I make a mistake in presentation.

Three logicians, who each use perfect logic, have a number written on their foreheads. None of them know what their own number is and are not allowed to tell eachother (obviously). They do know that each number is unique integer and that the sum of the lesser two equals the third. They stand in a circle and look at eachother's numbers. After a couple seconds of thought, one of the logicians asks the others if they know what their numbers are. After they say that they do not know, he announces, "My number is 50."

What are the numbers on the other 2 logicians' foreheads.

[/ QUOTE ]

This is interesting. I'd know the answer if the number one guys knows was dividable by 3, but 50 is not.
Thought process in white:
 The only way for one person to know something is if the two numbers he sees are such that one is twice the other. That way he knows he's the sum, because the larger number he sees can not be the sum, because then he and the smaller number must then be exactly the same, which is not the case according to rules.
Thus, for the speaker to know his number, one person has to have 1/3 of his number and the other 2/3 of his number.. and that doesn't work out to be integer.

And because other two are exactly as smart as him and they didn't know either, I don't see a solution.

ScottHoward

10-22-2006, 11:21 AM

three logicians numbers answer in white 20,30,50
log c figured out his number is 50, so we know a + b= 50. of all the numbers that add to 50, 20 and 30 are the only ones that allow for c to figure it out.with a-20,b-30, c must be 10 or 50,if c were 10, then b would know b was 10 or 30, and he cant be 10, so he would know hes 30. but b doesnt know his number so c then knows he is 50.

jstnrgrs

10-22-2006, 12:28 PM

[ QUOTE ]
[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Answer: "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. 

[/ QUOTE ] Or: There is an alternative answer. Ask one of them "If I were to ask you which way to go, what would you say?" Then go the way he says.

grando

10-26-2006, 06:46 AM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Answer: "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. 

[/ QUOTE ] Or: There is an alternative answer. Ask one of them "If I were to ask you which way to go, what would you say?" Then go the way he says. 

[/ QUOTE ]

well the liar will say the wrong way but the truthteller will tell you the right way....effective....

Toddy

10-26-2006, 10:21 AM

[ QUOTE ]
[ QUOTE ]
It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

[/ QUOTE ]

Answer: 40/13 days? [/quote

Please tell me this is for real

metsandfinsfan

10-26-2006, 10:44 AM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Answer: "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. 

[/ QUOTE ] Or: There is an alternative answer. Ask one of them "If I were to ask you which way to go, what would you say?" Then go the way he says. 

[/ QUOTE ]

well the liar will say the wrong way but the truthteller will tell you the right way....effective....

[/ QUOTE ]

well the first answer, "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. is 100% correct and works

metsandfinsfan

10-26-2006, 10:46 AM

This one has been posted before as well

10 Encylopedia are shelved in an orderly fashion. Each book contains 100 pages, numbered 1 through 100, with text on only one side per page. A bookworm starts eating at page 1 of book 1, and eats all the way through page 100 of book 10. Not counting covers, out of 1000 possible pages, how many pages did the bookworm eat through

jamzfive

10-26-2006, 11:28 AM

[ QUOTE ]
Not counting covers, out of 1000 possible pages, how many pages did the bookworm eat through

[/ QUOTE ]

Ans: 800 pages, and 18 of the 20 covers

metsandfinsfan

10-26-2006, 12:19 PM

[ QUOTE ]
[ QUOTE ]
Not counting covers, out of 1000 possible pages, how many pages did the bookworm eat through

[/ QUOTE ]

Ans: 800 pages, and 18 of the 20 covers

[/ QUOTE ]

not quite right, but you have the idea. And i said not counting covers, but your amount of covers was correct. Real close

jamzfive

10-26-2006, 01:45 PM

[ QUOTE ]
not quite right, but you have the idea. And i said not counting covers, but your amount of covers was correct. Real close

[/ QUOTE ]

OK, I re-read it:
It's 801 or 802. Page 100 of book 10 was eaten through, but it's not clear whether or not page 1 of book 1 was.

tabako

10-26-2006, 03:49 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Answer: "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. 

[/ QUOTE ] Or: There is an alternative answer. Ask one of them "If I were to ask you which way to go, what would you say?" Then go the way he says. 

[/ QUOTE ]

well the liar will say the wrong way but the truthteller will tell you the right way....effective....

[/ QUOTE ]

What? The truthteller will obviously tell you the right way, but so will the liar. The liar knows he would tell you the wrong answer to the question "Which is the right way?" so when you ask him "If I were to ask which way is the right way, what would you tell me?" he would have to lie about his answer, so he tells you the correct way.

metsandfinsfan

10-26-2006, 08:37 PM

[ QUOTE ]
[ QUOTE ]
not quite right, but you have the idea. And i said not counting covers, but your amount of covers was correct. Real close

[/ QUOTE ]

OK, I re-read it:
It's 801 or 802. Page 100 of book 10 was eaten through, but it's not clear whether or not page 1 of book 1 was.

[/ QUOTE ]

jam yes jam 802 is correct.

27offsuit

10-30-2006, 03:32 PM

I'm surprised this one hasn't shown yet:

Three men enter a hotel together and get 3 single rooms. The cost of each room is $10. They all pay and head to their respective rooms while the bellboy begins the task of bringing up their bags.

Just then the desk manager realizes he forgot to give them their $5 rebate special that they are advertising for three rooms. He gives the bellboy $5 and says "give this to those 3 gentlmen when you bring up their bags.

Bellboy is like "Crap, how do I spliy $5 three ways? Ah well, I'll just give them a dollar each and keep the left over $2." With that he goes up to each mans room, drops off his bags and gives them each $1.

Sooo...if they each get their rebate ($10 - $1 = $9) and the bellboy kept $2, that is only $29?

Where is the other $1?

metsandfinsfan

10-30-2006, 04:23 PM

[ QUOTE ]
I'm surprised this one hasn't shown yet:

Three men enter a hotel together and get 3 single rooms. The cost of each room is $10. They all pay and head to their respective rooms while the bellboy begins the task of bringing up their bags.

Just then the desk manager realizes he forgot to give them their $5 rebate special that they are advertising for three rooms. He gives the bellboy $5 and says "give this to those 3 gentlmen when you bring up their bags.

Bellboy is like "Crap, how do I spliy $5 three ways? Ah well, I'll just give them a dollar each and keep the left over $2." With that he goes up to each mans room, drops off his bags and gives them each $1.

Sooo...if they each get their rebate ($10 - $1 = $9) and the bellboy kept $2, that is only $29?

Where is the other $1?

[/ QUOTE ]

cause i think this one and the monty hall one have been posted so many times on 2+2 that you get instabanned for posting it

/images/graemlins/tongue.gif

ski

10-30-2006, 04:56 PM

ski

10-30-2006, 05:02 PM

[ QUOTE ]
three logicians numbers answer in white 20,30,50
log c figured out his number is 50, so we know a + b= 50. of all the numbers that add to 50, 20 and 30 are the only ones that allow for c to figure it out.with a-20,b-30, c must be 10 or 50,if c were 10, then b would know b was 10 or 30, and he cant be 10, so he would know hes 30. but b doesnt know his number so c then knows he is 50.

[/ QUOTE ]

Did you just get those numbers ( 20+30 ) through trial and error or is there some formula to it?

r3vbr

10-30-2006, 05:09 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
not quite right, but you have the idea. And i said not counting covers, but your amount of covers was correct. Real close

[/ QUOTE ]

OK, I re-read it:
It's 801 or 802. Page 100 of book 10 was eaten through, but it's not clear whether or not page 1 of book 1 was.

[/ QUOTE ]

jam yes jam 802 is correct.

[/ QUOTE ]

is this a word-game? didnt understand the answer.. why not 1000 pages?

baumer

10-30-2006, 05:20 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
here is a favorite of mine

You are rushing your mother to the hospital

There is a fork in the road and you dont remember which way to go

There are two twin brothers there, one who always lies and one who always tells the truth. They look identical, and it is impossible to tell them apart

You only have time to ask one brother one question. And again, the one who answers you have no idea if he is the one who lies or tells the truth

What one question can you ask so that no matter which brother answers, you will know which way to go to save your mother

[/ QUOTE ]

Answer: "If I asked your brother which way is it to the hospital, what would he say?" Then go in the other direction. 

[/ QUOTE ] Or: There is an alternative answer. Ask one of them "If I were to ask you which way to go, what would you say?" Then go the way he says. 

[/ QUOTE ]

well the liar will say the wrong way but the truthteller will tell you the right way....effective....

[/ QUOTE ]

What? The truthteller will obviously tell you the right way, but so will the liar. The liar knows he would tell you the wrong answer to the question "Which is the right way?" so when you ask him "If I were to ask which way is the right way, what would you tell me?" he would have to lie about his answer, so he tells you the correct way.

[/ QUOTE ]

I thought you were mistaken, but after reading this a couple times, it works. Just watched Labyrinth yesterday, had to chime in for no good reason.

Deorum

10-30-2006, 05:39 PM

[ QUOTE ]
I'm surprised this one hasn't shown yet:

Three men enter a hotel together and get 3 single rooms. The cost of each room is $10. They all pay and head to their respective rooms while the bellboy begins the task of bringing up their bags.

Just then the desk manager realizes he forgot to give them their $5 rebate special that they are advertising for three rooms. He gives the bellboy $5 and says "give this to those 3 gentlmen when you bring up their bags.

Bellboy is like "Crap, how do I spliy $5 three ways? Ah well, I'll just give them a dollar each and keep the left over $2." With that he goes up to each mans room, drops off his bags and gives them each $1.

Sooo...if they each get their rebate ($10 - $1 = $9) and the bellboy kept $2, that is only $29?

Where is the other $1?

[/ QUOTE ]

You miscalculated the total by adding the bellboy's cost twice. Each man paid $9, for a total of $27. That $27 cost is broken down into two parts: $25 for the total cost of the rooms plus $2 for the bellboy. The total allotment of the $30 is found by adding what they paid to what they received back, $27 + $3, not what they paid plus what they paid the bellboy, as what they paid the bellboy is already included in the cost of what they paid.

Deorum

10-30-2006, 05:51 PM

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not quite right, but you have the idea. And i said not counting covers, but your amount of covers was correct. Real close

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OK, I re-read it:
It's 801 or 802. Page 100 of book 10 was eaten through, but it's not clear whether or not page 1 of book 1 was.

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jam yes jam 802 is correct.

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is this a word-game? didnt understand the answer.. why not 1000 pages?

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Logic in white, if you want it:
 When placed on a bookshelf with the spine facing you, the first page of a book is located on the right hand side, and the last page is located on the left hand side. Thus, if the bookworm started on page one of the first volume, he did not eat pages 2-100 of that volume, and if he finished on page 100 of the tenth volume, he did not eat pages 1-99.

Deorum

10-30-2006, 05:55 PM

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One of my favorites from long ago, I hope I get it right. I have purposefully changed the usual wording to prevent easy googling:

A & B are integers greater than 1 and less than 100.

Mr. Add knows (A+B)
Mr. Multiply knows (A*B)

Mr. Add says to Mr. Multiply, "You don't know A and B."
Mr. Multiply says, "Now I do know A and B."
Mr. Add says, "Now I do too."

What are A & B?

~MagicMan

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I would really appreciate it if someone would please post the answer to this with the reasoning.

ScottySo

10-31-2006, 01:06 AM

alphatmw

10-31-2006, 01:21 AM

[ QUOTE ]
One of my favorites from long ago, I hope I get it right. I have purposefully changed the usual wording to prevent easy googling:

A & B are integers greater than 1 and less than 100.

Mr. Add knows (A+B)
Mr. Multiply knows (A*B)

Mr. Add says to Mr. Multiply, "You don't know A and B."
Mr. Multiply says, "Now I do know A and B."
Mr. Add says, "Now I do too."

What are A & B?

~MagicMan

[/ QUOTE ] A*B can't be prime, or else mr. multiply would know. thats where my ideas stopped. i also suspect that A*B must be less than 1600, as 1600 might be the largest number represented by two products of numbers between 1-100 (16*100 and 40*40).

Deorum

10-31-2006, 02:07 AM

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A*B can't be prime, or else mr. multiply would know.

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Also, A*B cannot be prime because the problem states that A and B are both greater than 1. Through my various attempts to solve this, I always get stuck between the first two statements: the first seems to imply that all possible sets of numbers derived from the sum that could be used as A and B have products that have at least five factors (including 1, which leaves us with 4 useful factors). For example, the sum cannot be 9, as the sets for A and B would then be {(2,7),(3,6),(4,5)} and the product of 2*7 is 14, which only has four factors. However, if all sets for A and B given by the sum of A and B have more than four factors, which I think is the implication of the first statement, "You do not know A and B", then he would need to be able to rule out all but one set of factors. I cannot figure out how he would do that.

alphatmw

10-31-2006, 02:58 AM

if the numbers were (3,4), then mr. add would see 7 and know that mr. multiply is seeing either 10 or 12. if he were seeing 10, he would know the numbers are 5,2 so he must be seeing 12. given that its 12, mr. multiply doens't know if its 6,2 or 3,4.

mr. multiply is seeing 12. he knows that it's either 6,2 or 3,4. if it were 6,2, mr add would be seeing 8 and would think its 2,6...3,5...or 4,4.

...(insert more complicated thoughts?!)...

therefore, mr. multiply knows it is not 6,2. thus he knows the numbers are 3,4. and once he figures that out, mr. add knows it's 3,4 also.

lol i thought i had it but the he thinks-i think-he thinks progession got too complicated. i think i might have the right answer though. i think A and B have to be between 1 and 10, and that OP said 1-100 to throw us off. i don't think multiplying numbers greater than 10 allow for this type of situation to be feasible.

then again, this is all speculation because i'm not smart enough to figure it out.

Magic_Man

10-31-2006, 12:04 PM

[ QUOTE ]
[ QUOTE ]
One of my favorites from long ago, I hope I get it right. I have purposefully changed the usual wording to prevent easy googling:

A & B are integers greater than 1 and less than 100.

Mr. Add knows (A+B)
Mr. Multiply knows (A*B)

Mr. Add says to Mr. Multiply, "You don't know A and B."
Mr. Multiply says, "Now I do know A and B."
Mr. Add says, "Now I do too."

What are A & B?

~MagicMan

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I would really appreciate it if someone would please post the answer to this with the reasoning.

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I have to admit that when I first saw this problem in high school, I mostly approached it with trial and error. That said, there are a few eliminations we can make:

1) Mr. Add knows that Mr. Multiply doesn't know A&B. This means that A*B is not the product of two primes, since it would then have a unique factorization.

2) Mr. Add must somehow then know that there is no combination of two primes A & B that make up his quantity (A+B). For example, A+B cannot be 12, because one possibility is A = 7, B = 5, both prime numbers. It just so happens that for "relatively small" numbers (certainly less than 100), any even number can be expressed as the sum of two primes (try it). Thus, A+B is odd. Notice that this means that A*B is even, since A & B must be a pair of odd & even numbers.

3) Also note that in order for Mr. Add's first statement to be true, A*B cannot be the cube of a prime. The only possible factors A & B would then be (prime1 * prime1^2). This, Mr. Add must see a number (A+B) that cannot be expressed as (prime1 + prime1^2).

4) We can now make a list of all possible numbers that Mr. Add sees. Start with the list 4, 5, 6 ... 198 and eliminate all numbers that can be expressed as the sum of two primes, or the sum of a prime and its square. Part of this list is:

(A+B) = 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97, ...

5) Now Mr. Product knows the numbers. This means that for some factors A*B, the quantity (A+B) is in the list above. If this were not true, then Mr. Sum could not have made his first statement. For example, if A*B = 16, the only choices are 4*4, and 2*8. 4+4 = 8 and 2+8 = 10, neither of which are in the list above. (They are not in that list because if (A+B) = 8, then there is a possibility A = 3, B = 5, in which case A*B = 15 and Mr. Product would know the two numbers immediately. Similar reasoning for A+B = 10. Again, A+B cannot be even.)

We can make a list of all the possibilities for Mr. Product, given this criterion. The fact that he actually found them means that for all the possible factors (A*B) that Mr. Product found, there is a unique number (A+B) that only occured once. Knowing this, Mr. Sum can find the two numbers, and they are:

Answer in white: A = 4, B = 13 

For a thorough explanation, see http://mathforum.org/library/drmath/view/55655.html

Or search google for "Mr. Sum and Mr. Product," since that is the traditional name of this puzzle.
~MagicMan

Magic_Man

10-31-2006, 12:13 PM

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It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

~MagicMan

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Obviously, this is a silly trick question. There's no such thing as half a hole; that would, in fact, be itself a hole.

~MagicMan

bigpooch

10-31-2006, 09:53 PM

Now that baseball season is over, maybe it's time for a
"baseball brain-teaser".

You are the team manager of a baseball team. You have nine
players on the roster that have unusual batting averages.
Call these players A, B, C, ..., I. It turns out that for
EACH of the last nine seasons, the batting averages of A,
B, C, ..., I are such that season after season,

the batting average of A was better than that of B,
the batting average of B was better than that of C,
...,
the batting average of H was better than that of I.

[By "better", I mean strictly better.]

Well, there's nothing usual about that so far. On the other
hand, each of these nine players had only played these nine
seasons, so it wasn't hard for you to compute their league
batting averages over all nine of these seasons. To your
surprise, the overall batting averages were such that

The league batting average for I was better than that for H,
the league batting average for H was better than that for G,
...
the league batting average for B was better than that for A.

How is this even possible?

Sephus

10-31-2006, 10:11 PM

players with higher career averages have more at bats in years where everyones averages were higher and/or fewer when their averages were lower?

bigpooch

11-01-2006, 04:44 AM

Could you yourself find an example using specific numbers,
or are you simply guessing?

Sephus

11-01-2006, 05:25 AM

if players can have any number of at bats in a given year then yes i believe that i myself could come up with an example using specific numbers, but i won't because i expect it to be too tedious.

Magic_Man

11-01-2006, 10:30 AM

Let's try it with three players:
Season 1:
A: AB: 10, H: 3, Avg = .300
B: AB: 8, H: 2, Avg = .250
C: AB: 6, H: 1, Avg = .167

Season 2:
A: AB: 10, H: 5, Avg = .500
B: AB: 50, H: 24, Avg = .480
C: AB: 100, H: 47, Avg = .470

Season 3:
A: AB: 10, H: 6, Avg = .600
B: AB: 100, H: 59, Avg = .590
C: AB: 200, H: 117, Avg = .585

League:
A: AB: 30, H: 14, Avg = .467
B: AB: 158, H: 85, Avg = .538
C: AB: 306, H: 165, Avg = .539

Extrapolate to 9 players.

~MagicMan

MatthewRyan

11-01-2006, 06:29 PM

shootaa

11-04-2006, 12:51 AM

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It takes 10 men 8 days to dig 13 holes. How long would it take one man to dig half a hole?

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answer in white:
 obv no such thing as 1/2 hole, one scoop = hole

BiPolar_Nut

11-04-2006, 03:00 PM

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We have 3 cannibals and 3 explorers and a boat that has the capacity for 2 ppl. How do you pass all 6 persons safely from one side fo the river to the other of the river?
If there is ever more cannibals than explorers on either side the cannibals will eat the explorers.

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Why not just do one of each on each trip??

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Because the boat is assumed to not have a "Return empty to other shore without getting swept down the river" device.

samsonite2100

11-05-2006, 01:01 AM

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We have 3 cannibals and 3 explorers and a boat that has the capacity for 2 ppl. How do you pass all 6 persons safely from one side fo the river to the other of the river?
If there is ever more cannibals than explorers on either side the cannibals will eat the explorers.

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answer in white below


1) CCC EEE
2) C EEE --------------------> CC
3) CC EEE <------------------ C
4) EEE ----------------------> CCC
5) C EEE <-------------------- CC
6) C E ----------------------> CC EE
7) CC EE <------------------- C E
8) CC -----------------------> C EEE
9) CCC <---------------------- EEE
10) C -----------------------> CC EEE
11) C E <--------------------- CC EE
12) -------------------------> CCC EEE