# Eight cards are on the table.

#### Speakpigeon

Valued Senior Member
Eight cards are on the table.

Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.

EB

Eight cards are on the table.

Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.
For even numbers? All of them. The last card could always have an even number.
For vowels? All of them. The last card could always have a vowel.

Are you leaving something out of your explanation, like each number or letter is only used once in a run of cards?

You would only need to turn over the 7 and 5.
You don't need to turn over the K, P, and R, because the requirement only concerns cards with a vowel.
You don't need to turn over the even numbers, because the requirement says nothing about non-vowels not also being allowed to have an even number on the other side.

You therefore only need to turn over the 7 and 5 because only the numbers on the other side of these cards can possibly show that the requirement is not being fulfilled.

Turn over all the cards that are currently showing numbers.

EDIT: On further examination, Baldee is correct, we only need to confirm that 5 & 7 are not vowels.

Turn over all the cards that are currently showing numbers.

EDIT: On further examination, Baldee is correct, we only need to confirm that 5 & 7 are not vowels.
Cue speakpigeon ranting about how you are not sticking to the OP by letting someone else's answer sway you.

Anyhoo, 5 and 7.
Reasons already given by my inestimable colleague Baldeee.

?

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Well, that was a quick thread.

Well, that was a quick thread.
I wanted to have one without having to insult people.
EB

I wanted to have one without having to insult people.
You never have to insult people...

if there is a vowel on one side, then there is an even number on the other side.

i wanted to go back to double check.
this proves that it is impossible

adding minus numbers to the total means the formula is unable to be quantified.

if you had not put minus numbers into the equation with the -4
then a probability would be possible to load as a set value of probability.
but you cant with an infinite range of odd & even numbers below 0

Huh? -4 is still an even number. There's an infinite number of odd and even numbers greater than zero, too.

Huh? -4 is still an even number. There's an infinite number of odd and even numbers greater than zero, too.

(below 10, e.g. 3, 7, 8 etc.)

whole numbers below 10
all minus numbers are whole ?
and even & uneven ?
infinity ?

i am not good at maths but that is my guess
-4 is even, but there is no total range of limit to even and odd by labeling the bottom level of whole minus numbers to complete the range ...

whole numbers below 10
all minus numbers are whole ?
and even & uneven ?
infinity ?

i am not good at maths but that is my guess
-4 is even, but there is no total range of limit to even and odd by labeling the bottom level of whole minus numbers to complete the range ...
From what you've written, I can't understand what you're objecting to.

Yes, there are whole numbers below 10.
No, all negative numbers are not whole numbers (integers).
Yes, some numbers below ten are even and others are odd.
Infinity doesn't appear to be relevant.
There is no range limit on positive numbers, any more than there is on negative numbers.
The original question does not in any way rely on a lower bound for potential integers on the cards.

From what you've written, I can't understand what you're objecting to.

Yes, there are whole numbers below 10.
No, all negative numbers are not whole numbers (integers).
Yes, some numbers below ten are even and others are odd.
Infinity doesn't appear to be relevant.
There is no range limit on positive numbers, any more than there is on negative numbers.
The original question does not in any way rely on a lower bound for potential integers on the cards.

I give up. I'm out.

RS: clearly, you are looking for some sort of pattern, but I suspect you are over-thinking it.
There is no restriction on what numbers can be applied here. They are simply grouped by odd and even.

Eight cards are on the table.
Each card has one capital letter (e.g. F, G, X etc.) on one side, and one number (below 10, e.g. 3, 7, 8 etc.) on the other side. At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.
What are the cards you really need to turn over to determine whether or not it's true of all the cards on the table that if there is a vowel on one side, then there is an even number on the other side.

OK, now, suppose no card has a vowel on it, either side.

How do you explain that we say it's true that if there is a vowel on one side, then there is an even number on the other side?
EB

-?
EB

OK, now, suppose no card has a vowel on it, either side.
How do you explain that we say it's true that if there is a vowel on one side, then there is an even number on the other side?
I'm not certain we do say that's true.
I'd want to see someone assert it before I try to explain why they might assert it.

At the moment, the cards show K, -4, 7, P, R, 0, 5, and 2.

?

if you require 2 known values to present a single answer
knowing that there is an infinite number of minus numbers, it makes it impossible.

you cant use infinity and add it to a probability scale to give an answer.
unless your using metaphors of thought and remove all the mathematics.
in which case your terms are not mathematical.

soo this then asks the question
"what is numbers?" answer = dont know = numbers mean nothing
"what is an alphabet?" = an alphabet is how we make sound for words to talk which is not mathematics.

you may as well be saying
i want you to start by imagining infinity.
once you have grasped infinity in your mind, hold it there and tell me when you have because im going to ask you a question about how it works.