Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A logical question

  1. Aug 12, 2008 #1
    on a table we arrange in a line four stones.
    two of them are small
    two of them are large
    two of them are green
    two of them are purple

    which one of the answers are not needed in order to determine the exact order of this stones?

    1.each green stone stayes between a big stone and a small stone
    2.both of the big stones are close one to the another
    3.the stone on the right edge is purple
    4.the green stones have the same size

    i dont know where to start
    how to deside what answer to start with??
    i dont know how to find this answer
    ??
     
  2. jcsd
  3. Aug 12, 2008 #2
    1st, try and figure out what the order is by looking at all the clues:

    1. "each green stone stayes between a big stone and a small stone"
    Well, #1 tells you quite a bit. Each green stone is between two stones, one big, one small. Hence, you can conclude that:
    A) neither green stone is on an end
    B) both green stones are in the middle
    C) because the stones are either green or purple, the stones on the ends are necessarily purple. So it goes Purple, Green, Green, Purple.
    D) the 1st and 3rd cannot both match in size
    E) the 2nd and 4th cannot both match in size
    F) The order is necessarily one of:
    - Big, Big, Small, Small
    - Big, Small, Small, Big
    - Small, Big, Big, Small
    - Small, Small, Big, Big

    That one clue told us a LOT.

    2. "both of the big stones are close one to the another"
    This tells us that the order is one of:
    - Big, Big, Small, Small
    - Small, Big, Big, Small
    - Small, Small, Big, Big

    3. "the stone on the right edge is purple"
    This tells us nothing new. Already, we know that this is the useless piece of information. All it tells us is that the order is one of:
    - Green, Green, Purple, Purple
    - Green, Purple, Green, Purple
    - Purple, Green, Green, Purple

    But we already know the EXACT order of the colors thanks to #1. Hence, without even looking at the rest of the clues, we know the answer is #3, because #3 told us only a small chunk of what #1 already told us. So any conclusion we can make with #3 could be equally made with #1, therefore #3 is extraneous. But we can keep going anyway.

    4. "the green stones have the same size"
    That's helpful. It doesn't tell us anything directly about the order, but with #1 and #3, it tells us exactly what we needed to know.

    All together
    With #1, we know the Color order is:
    Purple, Green, Green, Purple
    And we know the size order is one of:

    I. Big, Big, Small, Small
    II. Big, Small, Small, Big
    III. Small, Big, Big, Small
    IV. Small, Small, Big, Big

    So, after clue #1, all that remains is to figure out which order the sizes are in. With clue #2, we can eliminate possibility II, because the big stones must be close to each other. The remaining options are:
    I. Big, Big, Small, Small
    III. Small, Big, Big, Small
    IV. Small, Small, Big, Big

    With clue #4 (clue #3 tells us nothing new), we know that since the green's must have the same size, therefore the two in the middle must have the same size, hence eliminating possibilities I and IV. So the only remaining possibility is:
    III. Small, Big, Big, Small

    Clearly, because #3 told us something that we already learned from #1, #3 is a correct answer to the question. However, the question is (in our due diligence) whether #1 is necessary?

    Suppose we didn't have clue #1. We would know:
    2.both of the big stones are close one to the another
    3.the stone on the right edge is purple
    4.the green stones have the same size

    So we'd know the size order is one of:
    - Big, Big, Small, Small
    - Small, Big, Big, Small
    - Small, Small, Big, Big

    And we'd know the color order could be:
    - Green, Green, Purple, Purple
    - Purple, Green, Green, Purple

    But we wouldn't know which of those would be correct. Hence, #1 is clearly necessary (as it should be, since it told us a LOT of information).

    DaveE
     
    Last edited: Aug 12, 2008
  4. Aug 12, 2008 #3
    ye but we you also could say that the second answer comes from the first
    answer
    because one of the conclusions that comes from the first answer is that the first and third rocks differ in size
    and so does the 2nd and 4th.

    in the second answer we get the same conclusion
    so the 2nd one is unnecessary
    where is my mistake???
     
  5. Aug 12, 2008 #4
    i havnt bothered to work it out but if you dont know where to start
    to answer you question:

    leave out clue no.1
    can you solve with only clues 2,3,4

    if not then
    leave out clue no.2
    can you solve with only clues 1,3,4

    if not then
    leave out clue no.3
    can you solve with only clues 1,2,4
    etc etc

    eventually you'll find that you dont need one of the clues
     
  6. Aug 12, 2008 #5
    Are you sure this is not a homework in axiomatics?
     
  7. Aug 12, 2008 #6
    Close, but not quite.

    You're correct that the 1st and 3rd differ in size, and the 2nd and 4th differ in size, BUT that doesn't necessarily mean that the big stones are close together. Using only clue #1, a potential arrangement would be:

    Big, Small, Small, Big

    1st and 3rd differ in size (Big/Small), and 2nd and 4th differ in size (Small/Big), so it's totally valid, even though the two "Big" stones are as far apart as possible.

    DaveE
     
  8. Aug 13, 2008 #7
    thanks
    i understand your solution
     
  9. Aug 13, 2008 #8
    i dont know if this is axiomatics
    but i need to learn solving this kind of questions
    for "asat" exam in my country
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A logical question
  1. Logic question (Replies: 14)

  2. Logical Question (Replies: 9)

  3. Logical question (Replies: 7)

  4. Logical question (Replies: 4)

Loading...