Deductive Logic

Posted by: jgoo

Deductive Logic - 03/22/02 12:40 AM

Does anybody know where I can find some really challenging deductive logic puzzles? They're so much fun to solve and I can't find any. Thanks.
Posted by: Shadorunnr

Re: Deductive Logic - 03/22/02 03:00 AM

Two words; Rubics cube. Really challenging. And if you tell me that you can solve one in under two minutes, I'll pour mustard in your piano. ;\)
Posted by: aznxk3vi17

Re: Deductive Logic - 03/22/02 07:15 AM

RubiKs cube. Heh.

Really challenging logic puzzles? I'm afraid I don't have any... calculus is enough puzzling for me...
Posted by: nancyww

Re: Deductive Logic - 03/23/02 02:51 AM

Have you tried Dover? http://store.doverpublications.com/by-subject-puzzles--amusement--recreations-general.html
Posted by: Marquis de Posa

Re: Deductive Logic - 03/23/02 10:56 PM

You could pick up a book of Mensa puzzles; there are probably quite a few of those around. Some of the logic problems in these books are easy, but others are quite difficult. Here are a few examples of logic problems you'd find in these books:

1. In an election for class president, John is competing with two other candidates. After the election, the votes were tallied and it was found that each of the three candidates received exactly the same number of votes. However, there are rules that there could only be one president, and to settle this situation the three candidates agreed to draw a name out of a bag to determine who was going to be the winner. John takes a fresh piece of paper, writes one of the other candidates' names on the upper part of the sheet, his name in the middle, and the third candidate's name on the lower part of the sheet. He then tears the sheet of paper into strips so that each strip contains the name of one candidate. He places each of the strips into a bag and volunteers to draw the name of the winner. How does he ensure that he wins the election even though he is very adequately blindfolded?

2. A spy was captured by the enemy and was scheduled to be executed. Before the spy would be killed, he had the chance to make only one statement; if he told the truth, he would be hanged, and if he told a lie, he would be shot. The spy makes his statement, and afterwards, the enemy soldiers debate for hours about what to do and eventually decide to set the spy free. What did the spy say? (A very farfetched and unrealistic situation, but an excellent logic puzzle nonetheless.)

3. You have just left Venice and must travel to Rome by way of a desolate path that wanders through a thick forest. You travel down the path and come to a four-way intersection. There is a signpost that points the way to Rome and also points the way to Venice, but the signpost has been uprooted and is lying on the ground. There is nobody around for miles to ask for directions and you have no map or compass, and the night is cloudy so you are unable to look up into the sky to find the North Star. How do you figure out which path to take?

(Have fun trying to figure out the answers to these.)
Posted by: Brendan

Re: Deductive Logic - 03/23/02 11:20 PM

 Quote:
Originally posted by Marquis de Posa:
3. You have just left Venice and must travel to Rome by way of a desolate path that wanders through a thick forest. You travel down the path and come to a four-way intersection. There is a signpost that points the way to Rome and also points the way to Venice, but the signpost has been uprooted and is lying on the ground. There is nobody around for miles to ask for directions and you have no map or compass, and the night is cloudy so you are unable to look up into the sky to find the North Star. How do you figure out which path to take?
[/b]


Starve to death.

Seriously, though...go the opposite way that the sign is pointing to.
Posted by: Matt G.

Re: Deductive Logic - 03/23/02 11:37 PM

 Quote:
Originally posted by Marquis de Posa:
1. In an election for class president, John is competing with two other candidates. After the election, the votes were tallied and it was found that each of the three candidates received exactly the same number of votes. However, there are rules that there could only be one president, and to settle this situation the three candidates agreed to draw a name out of a bag to determine who was going to be the winner. John takes a fresh piece of paper, writes one of the other candidates' names on the upper part of the sheet, his name in the middle, and the third candidate's name on the lower part of the sheet. He then tears the sheet of paper into strips so that each strip contains the name of one candidate. He places each of the strips into a bag and volunteers to draw the name of the winner. How does he ensure that he wins the election even though he is very adequately blindfolded?[/b]


He feels for the strip with two ripped sides (the middle strip has his own name on it).
Posted by: JBryan

Re: Deductive Logic - 03/24/02 12:18 AM

 Quote:
2. A spy was captured by the enemy and was scheduled to be executed. Before the spy would be killed, he had
the chance to make only one statement; if he told the truth, he would be hanged, and if he told a lie, he would
be shot. The spy makes his statement, and afterwards, the enemy soldiers debate for hours about what to do
and eventually decide to set the spy free. What did the spy say? (A very farfetched and unrealistic situation, but
an excellent logic puzzle nonetheless.)


He says, "What I am about to say is the truth that is: what I have just said is a lie". You're right. Unrealistic. I would shoot the SOB anyway. \:D
Posted by: Marquis de Posa

Re: Deductive Logic - 03/24/02 01:21 AM

 Quote:
Originally posted by Matt G.:


He feels for the strip with two ripped sides (the middle strip has his own name on it).[/b]


Correct.
Posted by: Marquis de Posa

Re: Deductive Logic - 03/24/02 01:22 AM

 Quote:
Originally posted by JBryan:


He says, "What I am about to say is the truth that is: what I have just said is a lie". You're right. Unrealistic. I would shoot the SOB anyway. \:D[/b]


Close. But the answer I was looking for was a sentence of only four words.
Posted by: jgoo

Re: Deductive Logic - 03/24/02 02:50 AM

Thanks. I'll work on those, plus I'll visit that web site. In the meantime, heres one for the rest of you. Its fairly easy:

A man looks at a picture and says "Brothers and sons, I have none. But the father of this person is my fathers son." Who is he looking at in the picture?
Posted by: Marquis de Posa

Re: Deductive Logic - 03/24/02 04:01 AM

 Quote:
Originally posted by jgoo:
Thanks. I'll work on those, plus I'll visit that web site. In the meantime, heres one for the rest of you. Its fairly easy:

A man looks at a picture and says "Brothers and sons, I have none. But the father of this person is my fathers son." Who is he looking at in the picture?[/b]


He is looking at his daughter. He says he has no brothers, therefore, if the father of the person in the picture is his father's son, he must be the father of the person in the picture since he is the only person that would be eligible to be "his father's son." He has no sons, so the person in the picture is his daughter.
Posted by: jgoo

Re: Deductive Logic - 03/24/02 04:28 AM

 Quote:
Originally posted by Marquis de Posa:


He is looking at his daughter. He says he has no brothers, therefore, if the father of the person in the picture is his father's son, he must be the father of the person in the picture since he is the only person that would be eligible to be "his father's son." He has no sons, so the person in the picture is his daughter.[/b]


NOPE! Thats what I thought the first time that I read it, but its wrong. Read the clues a bit more carefully and think about them, and it will come to you. It took me a while, but I got the correct answer myself, and without looking at it first.
Posted by: Brendan

Re: Deductive Logic - 03/24/02 09:03 AM

 Quote:
Originally posted by jgoo:
"Brothers and sons, I have none. But the father of this person is my fathers son." Who is he looking at in the picture?[/b]


You told us the riddle wrong, jgoo. It's supposed to be "Brothers and sisters, I have none," not "Brothers and sons."

He is looking at a picture of himself.
Posted by: Brendan

Re: Deductive Logic - 03/24/02 09:03 AM

 Quote:
Originally posted by Marquis de Posa:


Close. But the answer I was looking for was a sentence of only four words.[/b]


"I'LL KILL YOU ALL!!!!!!!!"
Posted by: T2

Re: Deductive Logic - 03/24/02 09:57 AM

 Quote:
Originally posted by Brendan:


Starve to death.

Seriously, though...go the opposite way that the sign is pointing to.[/b]


Maybe you could examine the signpost for moss. If there is moss growing on the signpost it will be on the north side. Unless you are in Oregon, in which case it grows on all sides, and you are dead.
Posted by: JBryan

Re: Deductive Logic - 03/24/02 02:14 PM

 Quote:
Originally posted by Marquis de Posa:


Close. But the answer I was looking for was a sentence of only four words.[/b]


"This is a lie" or "I am now lying" or something to that effect.

"I will kill you" should get him hung since it is a true statement of his intentions no matter whether it is actually possible. In other words, it may be false but that does not make it a lie.
Posted by: mrenaud

Re: Deductive Logic - 03/24/02 02:55 PM

 Quote:
Originally posted by Marquis de Posa:
3. You have just left Venice and must travel to Rome by way of a desolate path that wanders through a thick forest. You travel down the path and come to a four-way intersection. There is a signpost that points the way to Rome and also points the way to Venice, but the signpost has been uprooted and is lying on the ground. There is nobody around for miles to ask for directions and you have no map or compass, and the night is cloudy so you are unable to look up into the sky to find the North Star. How do you figure out which path to take?[/b]


I assume that the signs to Venice and to Rome are attached to the same post. In that case I'd just plant the signpost into the ground with the sign to Venice pointing to where I came from. The sign to Rome should now correctly point to Rome.
Posted by: JBryan

Re: Deductive Logic - 03/24/02 03:04 PM

 Quote:
Originally posted by mrenaud:


I assume that the signs to Venice and to Rome are attached to the same post. In that case I'd just plant the signpost into the ground with the sign to Venice pointing to where I came from. The sign to Rome should now correctly point to Rome.[/b]


I actually thought of this but can it really be that easy? I assumed there was something I was not understanding correctly about the problem. It just does not seem like a very difficult problem if this is correct.
Posted by: Palindrome

Re: Deductive Logic - 03/24/02 03:22 PM

The guy who was (or was not) going to be shot might have said: "I will be released". If true, he gets to leave, if false, he's shot. Either way, the problem is solved. This is the only thing I can think of that would cause hours of discussion on the part of his captors.

I agree with the solutions of the other problems as given.
Posted by: jgoo

Re: Deductive Logic - 03/24/02 04:22 PM

 Quote:
Originally posted by Brendan:


You told us the riddle wrong, jgoo. It's supposed to be "Brothers and sisters, I have none," not "Brothers and sons."

He is looking at a picture of himself.[/b]


You got the answer correct. You've obviously seen the riddle before, if you knew that I told it wrong. I didn't realize when I wrote it. Oh well.
Posted by: Marquis de Posa

Re: Deductive Logic - 03/24/02 04:38 PM

 Quote:
Originally posted by mrenaud:


I assume that the signs to Venice and to Rome are attached to the same post. In that case I'd just plant the signpost into the ground with the sign to Venice pointing to where I came from. The sign to Rome should now correctly point to Rome.[/b]


Correct.
Posted by: Steve Miller

Re: Deductive Logic - 03/24/02 08:27 PM

Three men check in to a hotel room for the night, the cost of which is $30 for the night. Each man chips in $10, and up to the room they go.

Upon a change in managers, it is discovered that the men paid too much for their room - the actual cost of that room for a night is $25. The new manager sends the bellhop up to the room with 5 one dollar bills to refund the men their money.

The bellhop, being an enterprising young lad, decides to refund only $3, as trying to divide up $5 among three men would be too difficult. He pockets $2 for himself.

The three men are satisfied - each has now only paid $9 for their night in the hotel. But as 3 men x $9 each = $27, and the bellhop kept $2 for a total of $29, where did the other dollar go?
Posted by: nancyww

Re: Deductive Logic - 03/24/02 10:19 PM

 Quote:
Originally posted by Marquis de Posa:

2. A spy was captured by the enemy and was scheduled to be executed. Before the spy would be killed, he had the chance to make only one statement; if he told the truth, he would be hanged, and if he told a lie, he would be shot. The spy makes his statement, and afterwards, the enemy soldiers debate for hours about what to do and eventually decide to set the spy free. What did the spy say? (A very farfetched and unrealistic situation, but an excellent logic puzzle nonetheless.)
(Have fun trying to figure out the answers to these.)[/b]


"I will be shot"
Posted by: Marquis de Posa

Re: Deductive Logic - 03/24/02 10:42 PM

 Quote:
Originally posted by nancyww:


"I will be shot"[/b]


Correct.
Posted by: nancyww

Re: Deductive Logic - 03/24/02 10:44 PM

 Quote:
Originally posted by Steve Miller:
Three men check in to a hotel room for the night, the cost of which is $30 for the night. Each man chips in $10, and up to the room they go.

Upon a change in managers, it is discovered that the men paid too much for their room - the actual cost of that room for a night is $25. The new manager sends the bellhop up to the room with 5 one dollar bills to refund the men their money.

The bellhop, being an enterprising young lad, decides to refund only $3, as trying to divide up $5 among three men would be too difficult. He pockets $2 for himself.

The three men are satisfied - each has now only paid $9 for their night in the hotel. But as 3 men x $9 each = $27, and the bellhop kept $2 for a total of $29, where did the other dollar go?[/b]


The other dollar didn't go anywhere.

You start out with $30 ($10 from each man).

You end up with $30, too. The manager has $25 (the cost of the hotel room), the men have $3 (their refund of $1 each), the bellhop has the $2 (that he pocketed).

Yes, each man did end up paying $9 for the room, or $27 total for the 3 of them. That would be the $25 that went to the hotel manager and the $2 that the bellhop kept.

The confusion is caused by taking the $27 that the men paid and trying to add the $2 that the bellhop kept to make $29. Actually, you should subtract the $2 which would give you the $25 that the second manager ended up with for the room.

Gee, or maybe the confusion is in my explanation. Hope this makes sense. \:\)

[ March 24, 2002: Message edited by: nancyww ]
Posted by: Shadorunnr

Re: Deductive Logic - 03/25/02 01:58 AM

Here is an old puzzle...................There once was a racehorse that won great fame, what do you think was the horses name.
Posted by: Derick

Re: Deductive Logic - 03/25/02 03:01 PM

Here's one...

Every morning a man leaves his apartment on the 10th floor, enters the elevator and rides it down to the lobby. Every evening, upon returning home from work, the same man takes the elevator from the lobby to the 5th floor and then walks the remaining 5 flights of stairs. Why?

Derick
Posted by: mrenaud

Re: Deductive Logic - 03/25/02 03:16 PM

 Quote:
Originally posted by Derick:
Here's one...

Every morning a man leaves his apartment on the 10th floor, enters the elevator and rides it down to the lobby. Every evening, upon returning home from work, the same man takes the elevator from the lobby to the 5th floor and then walks the remaining 5 flights of stairs. Why?

Derick[/b]


Maybe because he's too short to reach the button to the 10th floor?
Posted by: DT

Re: Deductive Logic - 03/25/02 03:21 PM

I always thought there was the added proviso that he rode up to the 5th floor and walked the remainder unless it was raining.
Posted by: Derick

Re: Deductive Logic - 03/25/02 03:42 PM

Mrenaud is correct! Very good. You don't win anything but very good nevertheless!!!

DT - I never heard the puzzle augmented with "unless it was raining". Is there such a variation on this puzzle that you know the answer to?

Derick
Posted by: DT

Re: Deductive Logic - 03/25/02 04:12 PM

If it were raining, he had his umbrella with which he could reach the 10th floor button.
Posted by: Marquis de Posa

Re: Deductive Logic - 03/25/02 07:41 PM

Here are some more.

1. Here's a relatively easy one. I like tall women with long, curly black hair who listen to opera and dance very well. My coworker is tall, has long, curly black hair, listens to opera, and dances extremely well. My coworker and I also get along very well. I am a very confident young man who has no problem with asking women out on dates, and I have no policy against dating coworkers. But I would never even consider asking my coworker out on a date. Why is this?

2. You are wandering around in a very complex labyrinth. You come to a fork in the path on which you are travelling; one fork will lead to the exit of the labyrinth while the other one will lead to a giant man-eating turtle. There is no way of telling which path leads where. But fortunately, the devious creator of this labyrinth has placed two wise men who exist to only help adventurers who decide to enter the labyrinth, at the fork where you stand. The two wise men are exactly identical except for in one respect; everything one of them says is the truth, and everything the other one says is a lie. There is also no way of telling which wise man is the truthteller and which is the liar. You are only allowed to ask one question between the two of them. How do you find out which path will lead to the exit of the labyrinth?

[ March 25, 2002: Message edited by: Marquis de Posa ]
Posted by: wghornsby

Re: Deductive Logic - 03/25/02 07:58 PM

1. Is your coworker a guy?

2. Ask either one: "Which way would HE say is the exit?" And then take the opposite. Does that work?
Posted by: nancyww

Re: Deductive Logic - 03/26/02 06:09 PM

OK, here is a puzzle that had me baffled for quite a while. Maybe some of you will be able to figure it out right away. (I still can't even figure out what key I'm playing in). :rolleyes:

You have 12 balls and a balance-type scale. The balls all look identical but one weighs slightly more or less than the other 11. You have 3 chances to weigh the balls against eachother, in whatever combinations you choose. Can you determine which is the "oddball" and whether it is heavier or lighter than the rest? \:\)
Posted by: Marquis de Posa

Re: Deductive Logic - 03/26/02 06:20 PM

 Quote:
Originally posted by nancyww:
OK, here is a puzzle that had me baffled for quite a while. Maybe some of you will be able to figure it out right away. (I still can't even figure out what key I'm playing in). :rolleyes:

You have 12 balls and a balance-type scale. The balls all look identical but one weighs slightly more or less than the other 11. You have 3 chances to weigh the balls against eachother, in whatever combinations you choose. Can you determine which is the "oddball" and whether it is heavier or lighter than the rest? \:\)[/b]


First measurement: weigh four of the balls against another four of the balls. If the odd ball is on the scale, you would be able to see a difference in the weights of the two sides of the scale. Otherwise, if both sides weigh the same, the odd ball is among the four you have not weighed yet.

Second measurement: take the group of four balls that contains the odd ball. Weigh two of them against each other. If neither of these two balls are the odd ball...

Third measurement: measure the remaining two to find the odd ball.

Try the same thing with 27 balls and only 3 measurements.

Here's another puzzle; sort of difficult though...

Lisa likes 2 but not 22, 222, or 2222. She likes 109 but not 110. She likes 53 but not 35. She does not like 57 but likes 157. Would Lisa like 101 or 1001? And why?

[ March 26, 2002: Message edited by: Marquis de Posa ]
Posted by: Derick

Re: Deductive Logic - 03/26/02 06:31 PM

Lisa likes 101 because she likes prime numbers.

Derick
Posted by: nancyww

Re: Deductive Logic - 03/26/02 11:39 PM

 Quote:
Originally posted by Marquis de Posa:

Second measurement: take the group of four balls that contains the odd ball. Weigh two of them against each other. If neither of these two balls are the odd ball...
[ March 26, 2002: Message edited by: Marquis de Posa ][/b]


The first step is correct, weigh 4 against 4. Say that the side with #1-4 goes up and the side with #5-8 goes down. You do not know if the oddball is heavier or lighter than the rest. So now you must figure out if 1,2,3,or 4 is too light, or if 5,6,7,or 8 is too heavy.
Posted by: jgoo

Re: Deductive Logic - 03/27/02 12:44 AM

Here is a fairly easy one: A man lives in a small, one room house. Each of the four walls has one window. Each window faces toward the south. A bear walks past one of the windows. What kind of a bear is it?
Posted by: Shadorunnr

Re: Deductive Logic - 03/27/02 01:44 AM

jgoo..... it is a polar bear, at the north pole.-----hey doesn't anyone want to try at the racehorse question?? hint, the horse is fictious, so don't say manofwar or secratariout(sp?)
Posted by: Penny

Re: Deductive Logic - 03/27/02 02:08 AM

Mrs. Great Fame?

I'm really lousy at these!

penny
Posted by: Derick

Re: Deductive Logic - 03/27/02 02:12 AM

The horses name must be What-do-you-think right?

Derick
Posted by: jgoo

Re: Deductive Logic - 03/27/02 06:15 PM

 Quote:
Originally posted by Shadorunnr:
jgoo..... it is a polar bear, at the north pole.[/b]
Correct. Thats the only place in the world where all 4 windows could possibly face towards the south.
Posted by: Shadorunnr

Re: Deductive Logic - 03/28/02 02:46 AM

Derick, you are correct!
Posted by: Derick

Re: Deductive Logic - 03/28/02 04:51 AM

Here's a good one:

Nancy is a very attractive clerk in a candy store. She is 19 years old, is a Freshman at an Ivy League University, wears fashionable clothes, and is a highly competent mathematician. She has done a least squares analysis on her weight during the last two years and has found that the best fitting polynomial is a cubic equation. What does she weigh?

Derick
Posted by: DT

Re: Deductive Logic - 03/28/02 08:13 AM

She weighs candy.
Posted by: Derick

Re: Deductive Logic - 03/28/02 05:44 PM

Candy! Is that the answer? I came up with 115 lbs. Oh well. ;\)

Derick
Posted by: Marquis de Posa

Re: Deductive Logic - 03/28/02 08:39 PM

Here's a slightly easier version of the ball and scale puzzle that was posted earlier. You have 2187 balls (yes, that's two thousand one hundred eighty-seven) that are identical in every respect except for the fact that one of them is slightly heavier than all the rest. You have to find the heavy ball. The only device you have at your disposal in order to accomplish this is a balance that can only tell you whether the total weight of the objects you place on one side is greater than, equal to, or less than the total weight of the objects you place on the other side. You must complete the task in seven measurements.

(Note: assume the balance is large enough to hold as many balls as you want.)