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## Question

puzzle in book:all but 2 of my cars a fords all but 2 of my cars are toyotas and all but 2 of my cars are hondas how many cars do i have

3 cars

couldnt he have 2 cars and none of them be a honda toyota or ford?

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Good point, that is another way to look at the puzzle. The idea is that you have one of each car, but it works better when there aren't more than three things, like this one:

Two ducks in front of a duck, two ducks behind a duck, and a duck in the middle.

The answer to that one is 3, no question, but both your answer and the book's answer are correct for your puzzle.

Edited by Frost

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Yeah, I got that answer too

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hmm... both of the answers are right, but I think yours is more creative.

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couldnt he have 2 cars and none of them be a honda toyota or ford?

No. If you have no Fords, you can't make the statement "all but 2 of my cars are Fords". The statement requires that you do own at least one Ford. Likewise with Toyotas and Hondas; so you must have a Ford, Toyota and Honda. Saying "all but 2 of my cars are Fords" is equivalent to saying, "All of my cards are Fords, except for two of them".

The only answer that works is the one the book gave.

Since this is a discussion of a brain teaser, I'll move this to "New Riddles".

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Here is a puzzling contradiction that I conclude from your answer.

"If all but two of your cars are Fords and you have but two cars then there aren't any cars but those two neither of which are Fords"

For the record, I think 3 is the correct answer due to the implicit assumption that in order for a number of cars to be Fords, that number has to be a natural number. Of course, I am assuming the question meant "What is the fewest number of cars I could have?". If not, the answer is 17

Cheers!

--

Vig

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I am assuming the question meant "What is the fewest number of cars I could have?". If not, the answer is 17

17 doesn't work. If all your cars are Fords except for two, you have 15 Fords. You could not then say "all but 2 of my cars are Toyotas".

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If the universal quantifier all implies at least one, then the book, and Martini, are correct.

In some forms of logic - I believe the two that differ on this point are Aristotelian and boolean - is does not.

Thus, "All four-legged humans with three brains and two left hands are male" makes sense in - and is true in - boolean logic.

It is equivalent to the statement "No four-legged ... etc. are not male [female or androgenous]," which is more intuitively seen to be true.

In boolean logic, you can discuss all the members of empty sets.

But not in Aristotelian logic, where all implies at least one.

So the book probably took the Aristotelian view.

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No. If you have no Fords, you can't make the statement "all but 2 of my cars are Fords". The statement requires that you do own at least one Ford. Likewise with Toyotas and Hondas; so you must have a Ford, Toyota and Honda. Saying "all but 2 of my cars are Fords" is equivalent to saying, "All of my cards are Fords, except for two of them".

The only answer that works is the one the book gave.

Since this is a discussion of a brain teaser, I'll move this to "New Riddles".

Just my \$.02 but I would have to agree with Martini because of the statement "all but 2..."

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I've always understood that the statement "all X's are Y's" is equivalent to the statement "there are no X's that are not Y's." I would say that two is a possible answer.

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I've always understood that the statement "all X's are Y's" is equivalent to the statement "there are no X's that are not Y's." I would say that two is a possible answer.

Yeah.

What he said.

I vote boolean.

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"All but 2 of my cars are fords" implies that you have at least 1 ford car. (this is not an 'if-then' statement so that you can make the 'if' part false to make the statement true.)

However I am wondering about something else not related to this particular puzzle . Suppose we have just this statement "All but 2 of my cars are fords", and nothing else (forget about the toyotas and hondas). Now does this statement, "All but 2 of my cars are fords" implies that I have at least two non-ford cars? Or is it possible that all my cars are fords? What do you think?

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I've always understood that the statement "all X's are Y's" is equivalent to the statement "there are no X's that are not Y's."

So? How does that make 2 an acceptable answer?

If I have two Porsches (and no other cars) and said, "all but two of my cars are Fords", you would think that was an acceptable statement?

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I got the book answer...But your answer actually did come to mind as well. It's just, since it was in a book...They probably didn't intend on you thinking that outside the box.

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Suppose we have just this statement "All but 2 of my cars are fords", and nothing else (forget about the toyotas and hondas). Now does this statement, "All but 2 of my cars are fords" implies that I have at least two non-ford cars?

No, it implies that you have at least one Ford, just like in the riddle.

Or is it possible that all my cars are fords?

No, the statement "all but 2 of my cars are fords" means you have two care that are not Fords.

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So? How does that make 2 an acceptable answer?

If I have two Porsches (and no other cars) and said, "all but two of my cars are Fords", you would think that was an acceptable statement?

I would think it was a true, albeit poorly phrased, statement.

When I say that "all but two of my cars are Fords," that means that I own exactly two cars which are not Fords. If I own two Porsches, that statement is true. Suppose I invented a poison which I promised would kill all snakes in a given area. If there were no snakes in that area, was my promise broken?

EDITED for grammar and the last paragraph added

Edited by Chuck Rampart

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all but two of my cars are fords. <=> Remove two of my cars. All the remainder are fords.

In boolean logic, all the remainder may be discussed even though remainder is an empty set.

None of the remainder of my cars are non-fords.

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If the universal quantifier all implies at least one, then the book, and Martini, are correct.

Of course it does. The riddle was not written as a mathematical formula, it was written in English. If one says all of my cars are Porsches, and he has no cars- he's not telling the truth.

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Of course it does. The riddle was not written as a mathematical formula, it was written in English. If one says all of my cars are Porsches, and he has no cars- he's not telling the truth.

The statement is a categorical statement and it has logical import.

Logic is a disciple within which meaning may be deduced from categorical statements.

In one system of logic, the statement "All A are B" is equivalent to "No non-A are non-B".

Within that system no members of A are implied.

In another system of logic, "All A are B" implies there is at least one member of A.

So ... Sure it matters what system of logic you use.

If you don't define your terms and rules, you get endless and meaningless Brainden discussions.

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When I say that "all but two of my cars are Fords," that means that I own exactly two cars which are not Fords. If I own two Porsches, that statement is true.

Not in English.

Suppose I invented a poison which I promised would kill all snakes in a given area. If there were no snakes in that area, was my promise broken?

If your invention didn't exist, then yes. On more than one count. First, if there was no invention, you're already lying. Second, if you claimed it would kill snakes in a given area, that implies it would be effective regardless of whether or not there were snakes to kill. Saying that all your cars are Fords but two is okay to say when you have no Fords is just as inaccurate, grammatically speaking.

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all but two of my cars are fords. <=> Remove two of my cars. All the remainder are fords.

In boolean logic, all the remainder may be discussed even though remainder is an empty set.

None of the remainder of my cars are non-fords.

I think this is really a discussion on whether 0 can have units or not. When you have 0 objects and you specify units for them, you are simply stating that if you did in fact have 1 or more of those objects they would have the units that you stated. In the context of this riddle (as bonanova put it): "Remove 2 cars, the rest of them are now fords (even if there aren't any left)".

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all but two of my cars are fords. <=> Remove two of my cars. All the remainder are fords.

In boolean logic, all the remainder may be discussed even though remainder is an empty set.

None of the remainder of my cars are non-fords.

I think you are right and that means I was wrong in saying that "you have at least 1 ford car". That means all cars can be ford and also none of the cars can be ford. But then 'having no car' is also a plausible answer. Is it not?

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The statement is a categorical statement and it has logical import.

Logic is a disciple within which meaning may be deduced from categorical statements.

In one system of logic, the statement "All A are B" is equivalent to "No non-A are non-B".

Within that system no members of A are implied.

In another system of logic, "All A are B" implies there is at least one member of A.

So ... Sure it matters what system of logic you use.

If you don't define your terms and rules, you get endless and meaningless Brainden discussions.

Again, the riddle was not written as a formula; it was written in English. In English, if you say "all of my animals are dogs except for two", you are not telling a true statement if you don't own any dogs.

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"Remove 2 cars, the rest of them are now fords (even if there aren't any left)".

No cars = some Fords?

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No cars = some Fords?

If there were cars they would be Fords. However, there aren't any other cars and therefore there are no fords.

EDIT: They may be non existent, but they are still fords.

Edited by pw0nzd

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Again, the riddle was not written as a formula; it was written in English. In English, if you say "all of my animals are dogs except for two", you are not telling a true statement if you don't own any dogs.
Please read what I said.

You claim that something is or is not true. Truth is a logical entity. Your claim is a logical statement.

Without employing rules of logic, there is no way to determine whether or not your claim is a true statement - whether you are right or wrong.

I can write the following statement in English: two plus two equals five.

Now I claim my statement is true and I prohibit you from introducing the laws of arithmetic

by claiming that this is not an arithmetic statement; it was written in English and it is correct.

So ... two plus two equals five.

And please do not talk about rules of arithmetic to comment on whether the statement is correct - I wrote it in English, not in arithmetic.

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