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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 m

by 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.
- greggyb 11y ago
  We are presented with an actual situation. 4 visible cards on a table in front of us. I am not going full Descartes and claiming we cannot trust anything we see. We are told two things about the situation. You are assuming the first thing we are told can be trusted and the second can't. I understand that the logic puzzle is only to verify the second thing we are told. I am not confused. The way that the puzzle is presented, though, allows for confusion, because we are presented with three things: 1) A physical setup which can be trusted (4 cards exist, we see 1 side of each card) 2) A statement that each card has one color and one number 3) Even -> blue on other side. Given that one of the things we are expected to trust is a statement made to us and the thing we are expected to verify is a statement made to us, there is potential for confusion as to which statement(s) we are to verify. This potential is all that OP raised and all that I have been trying to explain. Edit: To summarize in brief, as the problem is presented, it is not 100% clear that some statements told to you by the experimenter can/should be trusted.
  - Nadya 11y ago
    Ah, I see the source of your confusion now. The actual situation as given to us is not that there are 4 visible cars on a table. It is that there are 4 visible cars on a table that contain a number on one side and a color on the other side. We are being told to verify the statement: "Of the 4 cards placed on the table, which have a number on one side and a color on the other side, if the number is even then the other side must be blue." If the color/number statement was left out of the original problem/video (it isn't) then your argument would be true, as it would be an assumption that is not listed and we would need to flip the 5 as well. E: And I suppose the blue card since it could have green on the other side.
    - greggyb 11y ago
      It seems, though that I was misinterpreting the original parent on this thread, though. I don't retract anything I said, but apparently his confusion was different.
ikeboy 11y ago
>If (1)must be verified then every card must be flipped. Actually, only the 5,8 and green. The blue is good no matter what. I saw this pedanticism in a Martin Gardner book originally, IIRC.
- greggyb 11y ago
  If (1) must be verified, how can you know that the blue card has a number on the other side? To verify (1) you must prove that each card has a color on one side and a number on the other. The only way to do this is to see both sides of each card.
  - ikeboy 11y ago
    Oh, you mean actually verifying 1. I wasn't doing that. I was just doubting 1 being true, but interpreting the problem as asking you to verify 2, in which case you only need to turn over 5,8, and green.
    - greggyb 11y ago
      Okay, now I'm really confused about what you meant with your original post in this thread. If you doubt (1), how is it that you need to verify that the 5 has a color, but not that the blue has a number on the other side? To verify (2) you only need to prove that every even card has a blue back. An odd may be blue or green, but an even must be blue. Hence the 5 is fine, it can have any color. The blue is fine, because it can have any number. But that 8 must have a blue back, and that green must have an odd number.
      - ikeboy 11y ago
        >The problem with this is that the 5 card also needs to be turned; it might have an even number on the back. If you can't be sure that the cards have a color and a numbers, there's nothing outlawing a 5-6 card, which breaks (2).
        11y ago

by greggyb 11y ago

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.

greggyb 11y ago
We are presented with an actual situation. 4 visible cards on a table in front of us. I am not going full Descartes and claiming we cannot trust anything we see. We are told two things about the situation. You are assuming the first thing we are told can be trusted and the second can't. I understand that the logic puzzle is only to verify the second thing we are told. I am not confused. The way that the puzzle is presented, though, allows for confusion, because we are presented with three things: 1) A physical setup which can be trusted (4 cards exist, we see 1 side of each card) 2) A statement that each card has one color and one number 3) Even -> blue on other side. Given that one of the things we are expected to trust is a statement made to us and the thing we are expected to verify is a statement made to us, there is potential for confusion as to which statement(s) we are to verify. This potential is all that OP raised and all that I have been trying to explain. Edit: To summarize in brief, as the problem is presented, it is not 100% clear that some statements told to you by the experimenter can/should be trusted.
- Nadya 11y ago
  Ah, I see the source of your confusion now. The actual situation as given to us is not that there are 4 visible cars on a table. It is that there are 4 visible cars on a table that contain a number on one side and a color on the other side. We are being told to verify the statement: "Of the 4 cards placed on the table, which have a number on one side and a color on the other side, if the number is even then the other side must be blue." If the color/number statement was left out of the original problem/video (it isn't) then your argument would be true, as it would be an assumption that is not listed and we would need to flip the 5 as well. E: And I suppose the blue card since it could have green on the other side.
  - greggyb 11y ago
    It seems, though that I was misinterpreting the original parent on this thread, though. I don't retract anything I said, but apparently his confusion was different.

ikeboy 11y ago

>If (1)must be verified then every card must be flipped. Actually, only the 5,8 and green. The blue is good no matter what. I saw this pedanticism in a Martin Gardner book originally, IIRC.

greggyb 11y ago
If (1) must be verified, how can you know that the blue card has a number on the other side? To verify (1) you must prove that each card has a color on one side and a number on the other. The only way to do this is to see both sides of each card.
- ikeboy 11y ago
  Oh, you mean actually verifying 1. I wasn't doing that. I was just doubting 1 being true, but interpreting the problem as asking you to verify 2, in which case you only need to turn over 5,8, and green.
  - greggyb 11y ago
    Okay, now I'm really confused about what you meant with your original post in this thread. If you doubt (1), how is it that you need to verify that the 5 has a color, but not that the blue has a number on the other side? To verify (2) you only need to prove that every even card has a blue back. An odd may be blue or green, but an even must be blue. Hence the 5 is fine, it can have any color. The blue is fine, because it can have any number. But that 8 must have a blue back, and that green must have an odd number.
    - ikeboy 11y ago
      >The problem with this is that the 5 card also needs to be turned; it might have an even number on the back. If you can't be sure that the cards have a color and a numbers, there's nothing outlawing a 5-6 card, which breaks (2).
      - 11y ago