You and two friends are having an argument about which of you is the smartest, so you ask a Grand Master Logician (Mike) to set up a completely fair test to reveal the smartest amongst you. Mike shows all three of you 5 hats - two red and three black. Then he turns off the lights in the room, puts a single hat on each person's head (except his own), and hides the remaining two hats. When Mike turns the lights back on, each of you is able to see the hats on the other two people's heads, but you cannot see the hat on your own head. The winner is the person who first guesses the correct color of his own hat. Each person can guess only once. What is your strategy for winning the contest?

• The above question is about the strategy not the probability!! one can say the correct answer that his hat is black , if he see red hats on the other two. if they see two black hat then he might be wearing red and blak or both blak.
• 11 years agoHelpfull: Yes(12) No(1)
• 2 red and 3 black hats Onlyif other 2 persons has red hats on their heads the 3rd person can guess his hates color thus 2 hats are red in color 2P2*3P1
  Total possibilities are 5P3 thus winning strategy is (2P2*3P1)/5P3 =1/10=10%
• 11 years agoHelpfull: Yes(9) No(2)
• 
  all the eight possibilities of hats, listed below, on the
  heads of the persons are equally likely
  
  
  possibilities person1 p2 p3 Probability
  1 Red Red Red 1/8
  2 Red Red Black 1/8
  3 Red Black Red 1/8
  4 Red Black Black 1/8
  5 Black Red Red 1/8
  6 Black Red Black 1/8
  7 Black Black Red 1/8
  8 Black Black Black 1/8
  to understand this problem , let us take an example :
  in this example all have d same instructions
  a. If the colors of hats of both friends are red, say that the color
  of your hat is black.
  b. If the colors of hats of your friends are both black, say that the color
  of your hat is red.
  c. If the colors of hats of your team mates are different, pass
  Actual Configuration Responses Outcome
  p1 p2 p3 p1 p2 p3
  R R R B B B Loss
  R R B P P B Win
  R B R P B P Win
  R B B R P p Win
  B R R B P P Win
  B R B P R P W in
  B B R P P R Win
  B B B R R R Loss
  
  
  It is now clear that the chances of winning the prize under this strategy
  are 75 per cent.
  this is one of the strategy
• 11 years agoHelpfull: Yes(4) No(10)
• 2/3 i think.
• 11 years agoHelpfull: Yes(0) No(5)
• My strategy depends on what I see on other two heads AND what my two friends will say (yes or no) when I ask them a question if they are able to figure out their own color.
  1. If I see two red I am black, this was the easiest and I can call right away and win.
  2.If I see one black and one red and if they both say no as an answer to my question that means I am black. If one say yes and other no that means I am red.
  3. If I see both black hats no matter what I wear their answer will be no and I will have 100% chance to guess the right color on my head or I am missing something, I really would like to see the solution.
• 10 years agoHelpfull: Yes(0) No(0)
• Oops I was thinking to say "I will NOT have 100% chance to figure out my own color", just 50% for guessing out of two colors.
• 10 years agoHelpfull: Yes(0) No(0)