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Brainteaser 01

  1. Mar 31, 2011 #1
    Five people, Albert, Bob, Terry, Christine, and Noah, each have one red hat on their heads from a pile that originally had two blue, two green, and five red hats. Each can see the others' hats but cannot see his or her own. Albert eventually deduces that he has a red hat on.

    How did he know? Assume that all five people are reasonably intelligent and logical.

    As long as you explain your though process and it's rational I don't see why it wouldn't be correct. So there might be more than one correct answer.
  2. jcsd
  3. Mar 31, 2011 #2
    Could it be that Albert sees that collectively Bob, Terry, Christine and Noah are wearing two blue and two green hats?
  4. Mar 31, 2011 #3
    It's given that they're all wearing white.
  5. Apr 1, 2011 #4
    1- He can see the pile of hats.
    2- Blue hats and Green hats are funny. As nobody is laughing, he knows he's wearing a red hat.
    3- They are linuxers and don't know how to apt-getting...so...
  6. Apr 1, 2011 #5


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    Homework Helper

    1) Albert can see the pile of hats.
    2) Bob told Albert that he's wearing a red hat, since Bob blabs a lot.
    3) The group switched hats shortly after wearing them.
  7. Apr 2, 2011 #6
    Albert, Bob, Terry, Christine, and Noah

    Since Albert does not know his colour,he will just randomly try to assume one of them and see if it fits the conditions

    So let us assume he thinks his hat to be blue
    Now Albert thinks as follows:
    If I was blue,and Bob thinks himself to be blue,then
    (going into Bob's mind through Albert's mind,i.e. this is a cycle going on where Albert is still the main thinker and he wears Bob's shoes).....
    Albert thinks that Bob will think:
    -----> Since Albert is blue and I am blue too,Terry will think that:

    Albert thinks that Bob will think that Terry will think:Since there are two blue hats,mine is not blue and the other too are reds,so if i was green

    Albert thinks that Bob will think that Terry will think that Christine will think:Albert and Bob are blue,Terry is green and Noah is red,so if was green too:
    (All this while Albert is the "only" thinker)
    Since Albert waits and no one is able to figure out his colour,he can prove that he is not blue or green....so he knows that he is red!
  8. Apr 2, 2011 #7
    I guess that works
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