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The confusion doesn't arise from missing the statement you quoted, but whether this is to be treated as part of the problem statement that you are testing for t

by greggyb 11y ago

The confusion doesn't arise from missing the statement you quoted, but whether this is to be treated as part of the problem statement that you are testing for truth. If you can take it as absolute truth that each card has a number on one side and color on the other, then you only have to check which color. If on the other hand you must verify both that each card has one color/one number and that even cards have blue on the back, then you must turn over every card to ensure that each has the expected quality of opposite side (i.e. that if you see a number, the opposite side has a color and vice versa).

coldtea 11y ago
>The confusion doesn't arise from missing the statement you quoted, but whether this is to be treated as part of the problem statement that you are testing for truth. You are not supposed to test for truth the problem premises. Just the if "even then blue" statement. If you also had to test the premises then there would be no question and no asnwer -- because those require premises.
- greggyb 11y ago
  See sibling threads. Short version: You are presented with 4 cards on a table. You can see one side of each card. You are told two things: 1) Each card has a number on one side and a color on the other side. 2) If a card has an even number, then its color is blue. It is not unreasonable assume that you are expected to verify all things you have been told (i.e. all things you cannot verify by what you observe). Since you know you can't trust the second thing you are told about the cards, why should you assume that the first thing you are told about the cards is true? OP is saying that you cannot trust anything you've been told, and is attempting to verify (2) without trusting (1). I misinterpreted and assumed that OP was saying the goal to verify all statements that you've been told.
  - coldtea 11y ago
    No, you're told these things: 1) Each card has a number on one side and a color on the other side. 2) Pick the minimum numbers of cards needed to verify the statement "If a card has an even number, then its color is blue". >Since you know you can't trust the second thing you are told about the cards, why should you assume that the first thing you are told about the cards is true? This reading doesn't make any sense. If you were indeed given (1) and (2) in that form, and indeed couldn't trust them both, then there would be no quiz at all. Just 2 random sentenses that might or might not be true.
    - greggyb 11y ago
      In the setup, you are presented with four actual cards in front of you, two where you can see a number, and two where you can see a color. This is verifiable with your senses. You are then told two statements about these cards and asked to verify the second statement. As OP of this thread pointed out, the card with 5 must be checked, because it's possible that it has an even number on its reverse side. I originally misinterpreted the OP as saying that both (1) and (2) must be verified. You can see the two sibling branches that explore both of these in much more depth and back and forth.
Nadya 11y ago
You are told each card has a number on one side and a color on the other. The statement is mentioned in other words in the article - but what I quote is from the very first sentence of the YouTube video used to demonstrate the problem. The confusion comes from making an assumption that if a card is odd then it cannot also be blue. if even then blue //what is being asked if even then blue && if odd then !blue //what people assume
- greggyb 11y ago
  I understand the logic and confusion you are presenting. The confusion that I am referring to is what portion of the problem statement can be trusted and what must be verified. The situation follows: 1) There are four cards with a number on one side and a color on the other. 2) If a card has an even number on one side, then it's blue on the other. You are only allowing for confusion about the commutative nature of the conditional in (2); it is not commutative, but a common false assumption is that it is. What the parent of this thread is referring to is that there can be confusion regarding whether (1) must also be verified. If (1)must be verified then every card must be flipped.
  - Nadya 11y ago
    (1) only needs to be verified when it is not a part of the problem. "If Jenny has 5 apples and Bob has 5 apples and Jenny gives Bob 2 apples - how many apples does Jenny now have?" We don't question if Jenny went and bought n more apples to give to Bob and might have 3 Apples or 5 Apples or 5+n where n is the number of apples purchased minus 2 because it isn't part of the problem and isn't part of what is being asked. Maybe she won an apple lottery and that is why she gave Bob 2 apples. Maybe she gave Bob 2 apples and later lost her other 3 apples in a fire. If you begin by questioning the validity of the question - Jenny can have 0...n apples. Which doesn't do us any good for solving the problem. "There are four cards. Each card has a number on one side and a color on the other side." These details are taken as facts as a basis for solving the problem. If you are questioning if there is a color and number on the sides. Are there really 4 cards? What if there is a 5th card I'm not told about? What if we took 4...n cards and I found a card that invalidates the problem? It's ignoring the problem and coming up with a new one to solve.

by greggyb 11y ago

coldtea 11y ago

>The confusion doesn't arise from missing the statement you quoted, but whether this is to be treated as part of the problem statement that you are testing for truth. You are not supposed to test for truth the problem premises. Just the if "even then blue" statement. If you also had to test the premises then there would be no question and no asnwer -- because those require premises.

greggyb 11y ago
See sibling threads. Short version: You are presented with 4 cards on a table. You can see one side of each card. You are told two things: 1) Each card has a number on one side and a color on the other side. 2) If a card has an even number, then its color is blue. It is not unreasonable assume that you are expected to verify all things you have been told (i.e. all things you cannot verify by what you observe). Since you know you can't trust the second thing you are told about the cards, why should you assume that the first thing you are told about the cards is true? OP is saying that you cannot trust anything you've been told, and is attempting to verify (2) without trusting (1). I misinterpreted and assumed that OP was saying the goal to verify all statements that you've been told.
- coldtea 11y ago
  No, you're told these things: 1) Each card has a number on one side and a color on the other side. 2) Pick the minimum numbers of cards needed to verify the statement "If a card has an even number, then its color is blue". >Since you know you can't trust the second thing you are told about the cards, why should you assume that the first thing you are told about the cards is true? This reading doesn't make any sense. If you were indeed given (1) and (2) in that form, and indeed couldn't trust them both, then there would be no quiz at all. Just 2 random sentenses that might or might not be true.
  - greggyb 11y ago
    In the setup, you are presented with four actual cards in front of you, two where you can see a number, and two where you can see a color. This is verifiable with your senses. You are then told two statements about these cards and asked to verify the second statement. As OP of this thread pointed out, the card with 5 must be checked, because it's possible that it has an even number on its reverse side. I originally misinterpreted the OP as saying that both (1) and (2) must be verified. You can see the two sibling branches that explore both of these in much more depth and back and forth.

Nadya 11y ago

You are told each card has a number on one side and a color on the other. The statement is mentioned in other words in the article - but what I quote is from the very first sentence of the YouTube video used to demonstrate the problem. The confusion comes from making an assumption that if a card is odd then it cannot also be blue. if even then blue //what is being asked if even then blue && if odd then !blue //what people assume

greggyb 11y ago
I understand the logic and confusion you are presenting. The confusion that I am referring to is what portion of the problem statement can be trusted and what must be verified. The situation follows: 1) There are four cards with a number on one side and a color on the other. 2) If a card has an even number on one side, then it's blue on the other. You are only allowing for confusion about the commutative nature of the conditional in (2); it is not commutative, but a common false assumption is that it is. What the parent of this thread is referring to is that there can be confusion regarding whether (1) must also be verified. If (1)must be verified then every card must be flipped.
- Nadya 11y ago
  (1) only needs to be verified when it is not a part of the problem. "If Jenny has 5 apples and Bob has 5 apples and Jenny gives Bob 2 apples - how many apples does Jenny now have?" We don't question if Jenny went and bought n more apples to give to Bob and might have 3 Apples or 5 Apples or 5+n where n is the number of apples purchased minus 2 because it isn't part of the problem and isn't part of what is being asked. Maybe she won an apple lottery and that is why she gave Bob 2 apples. Maybe she gave Bob 2 apples and later lost her other 3 apples in a fire. If you begin by questioning the validity of the question - Jenny can have 0...n apples. Which doesn't do us any good for solving the problem. "There are four cards. Each card has a number on one side and a color on the other side." These details are taken as facts as a basis for solving the problem. If you are questioning if there is a color and number on the sides. Are there really 4 cards? What if there is a 5th card I'm not told about? What if we took 4...n cards and I found a card that invalidates the problem? It's ignoring the problem and coming up with a new one to solve.