3 prisoners 3 hats riddle Unfortunately, the Warden had no exposure to probability theory. This is comparable to the Monty Hall problem. Prisoner 3 is facing a wall and cannot see anyone’s hat. ted. The prisoners will not be able to see their own hats and the only way they can work out what colour hat they are wearing will be from looking at the hats the other prisoners are wearing. Since A, B, and D are silent, that leaves C. e. If the prisoners don’t know the answer, they keep quiet. A sees B & C, B sees A & C, and C sees A & B. The prisoner in the back can clearly see all 99 hats in front of him. Each prisoner is wearing a hat of color either black or red. Once outside the closet, no man can see his own hat. Number 3 sees only the wall. Since prisoner 2 could not reason his hat color, it must be the case that prisoner 3 is not wearing a blue hat, resulting in only 4 cases. Also called the “prisoner hat” riddle, the “four hat” riddle begins with four prisoners who have all been lined up, one behind the other and all facing in the Feb 16, 2017 · The prisoners cannot see the color of the hat on their own head, but they can see the colors of all the hats in front of them. They know that their placement in this room is as follows: In a variant of this puzzle, the prisoners know that there are 3 hats of one color and only 1 hat of another, and the 3 prisoners can see each other i. In this version, you and nine other humans have been abducted by aliens. Oct 6, 2023 · The “four hat” riddle. The jailer is going to ask colo 12. The only permutation where the 3rd prisoner could have a RED hat and the 2nd prisoner NOT have a WHITE hat is permutation 1, which is already ruled out already in (1). Inside of a dark closet are five hats: three blue and two red. Let's kick off the new month with one of my favorites, a question of life or death. All four men wear hats; there are two black hats and two white hats, each prisoner is wearing one of the hats, and each of the prisoners see only the hats in front of him but neither on himself nor behind him. Prisoner one stays silent because they see two different hats. youtube. After a while, A shouts out the (correct) color of his hat !! Explain. The first of the 3 to solve t Prisoner A only has a ⁠ 1 / 3 ⁠ chance of pardon. Same logic for next 2 prisoners as well Now the sixth prisoner from last see number of white hats as 2:(even)-> he can say it is his hat which was making the white at count odd, so his hat The man in the back sees the middle man with a white hat and the front man with black hat, 2 black hats and 1 white hat remain, so he guessed black, but was actually wearing white, now middle man knows the back man had white and see the guy in front has a black hat so he figures the same way, twice as likely to have a black hat on, but he is We would like to show you a description here but the site won’t allow us. Number 2 sees number 3’s hat. Three of the hats are black and two of the hats are white. The first man, let’s call him A, at the rear, can see both other men and their hats. Preparation for the test being over, blindfolds are removed, and the Chief explains the game to the prisoners. Each man will have a hat placed on his head while blindfolded. The two hats left over are hidden. After he hears B will be executed, Prisoner A realizes that if he will not get the pardon himself it must only be going to C. The riddle is also popular with the name “Google Prisoners Hat Riddle”. Brody Dylan Johnson Saint Louis University The Hat Problem Jan 19, 2023 · Similarly other prisoners from 97 to 1 are saved. He then turns out the lights, puts a hat on each prisoner and puts the other two hats in an opaque box. Person 1 can see the blue hat on 3, but also knows person 2 has a blue A hat is put on each of their heads. Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. So there are 4C2 = 4!/(2!2!) = 6 ways the hats could be arranged. The prisoners win when at least one correct guess is made and no incorrect guesses are made. That means there is a 2/3 chance for C to get a pardon. Problem. If the two front hats were black, the third wise man would have called out the colour of his hat as white immediately. All Aug 16, 2009 · Actually, the "100% sure" part is pretty presumptuous. RRR RBR BRR BBR. ) There is a wall between prisoners C and D (which cannot be seen through or around). But since D is silent, C knows that he must be wearing a black hat as he can see that B is wearing a white hat. Nov 2, 2022 · The Three Prisoners Puzzle — Challenge. Riddle: There are four prisoners. None of the prisoners can see his own hat, and all are intelligent. Solution: Mar 19, 2016 · In this TED-Ed lesson, Alex Gendler walks us through the "prisoner hat riddle," a classic puzzle. A prisoner can see hats of all prisoners in front of him in the queue, but cannot see his hat and hats of prisoners standing behind him. So if the Three of the men stand a line. No communication is allowed between prisoners, including whether or not others have elected to guess or pass. A faces the wall, B faces A, and C faces B and A. From this Prisoner 2 infers that their hat is a different Two white and two black. In both of these cases, prisoner 2 is wearing a red hat. Here is the correct answer with proper explanation to this “4 Prisoners Hat Riddle”. When each man is wearing a hat the blindfolds will be removed. If the first hat were black, and the third man did not call out any colour, the second wise man could deduce that his hat was white. Jul 14, 2021 · The prisoners are now blindfolded, and a hat is placed on the head of each. Out of 7 hats, 3 were black and 4 white. Knowing whether B or C will be executed does not change his chance. T hat night, the Warden thought long and hard about Arun’s request. The prisoners are immobilized in the ground and can't twist their body to see the person behind them. Jan 31, 2024 · Number 1 sees number 2 and 3’s hats. Dec 1, 2016 · Welcome back to Popular Mechanics' series of weekly riddles. com/lessons/can-you-solve-the-prisoner-hat-riddle-alex-gendlerWant more? Try the buried treasure riddle: https://www. (D again not to be seen and only there to wear the last hat. They all know that there are 2 black hats and 2 white hats, and that there are four people. Details of the Game: 4 prisoners and hats logic puzzle. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered. Jul 30, 2014 · Number 1 sees number 2 and 3's hats. Prisoners C and D see only the wall. OR. A prisoner sees all of the hats, except his or her own. " The cannibals show the men five hats. There are no mirrors. All they know is that there are 4 people Jan 18, 2023 · 100 prisoners in jail are standing in a queue facing in one direction. A fourth man is put behind a wall. Aug 20, 2010 · The jailer comes in, and shows the prisoners 5 hats: two red and three black. Number 4 sees only the wall. The first man looks at the other two, thinks, and says, "I cannot tell what color my hat is. The riddle remains the same and the question and the step by step explanation is given below. A hat is placed on the head of each. Nov 30, 2024 · If prisoner 2 saw a blue hat on prisoner 3, then the only corresponding cases would be: RRB BRB. Knowing this, three smart men go into the closet, and each selects a hat in the dark and places it unseen upon his head. Apr 24, 2021 · Prisoners Hat Riddle is very interesting riddle. Aug 23, 2016 · That is, if the 3rd prisoner has a RED hat, the 2nd prisoner would know that either permutation 2 or permutation 3 is correct, and either way, his hat must be WHITE. rrbb rbrb rbbr bbrr brbr brrb. rbrb bbrr brrb. The second man, B, in the middle, can see only the last man and his hat. They are told that each of these hats was selected from a group of five hats: three black hats and two white hats. Prisoner A can see prisoners B and C (by moving his head to the side). If the first two people received white hats, and the 3rd prisoner was rather dumb, or if the 3rd prisoner wanted the 2nd prisoner to incorrectly guess that his hat was black, the 3rd prisoner could just sit there and wait for 5 minutes before saying anything, even though he has all the data necessary to guess his own hat color. Apr 20, 2013 · Again for the next prisoner: number of white hats in front of him: 3(odd), as the the previous prisoner said black so it must be black hat on his head too. The aliens would like to . However, prisoner 2 can only see the hat of prisoner 3. (1/3) to one Oct 19, 2023 · Once 2 blue hats are placed, the other 2 spots will be red hats. The jailer tells the prisoners that if they can correctly guess the color of their own hat (which they will not be able to see), they will be set free. To these three prisoners he would present a riddle. They could come up with a strategy where initially two random guys stands at the front, then if both of them have the same color then the third will stand behind them, and in between them if their hats are of different color, now the 4th guy will also do the same, he will stand at a position where hat color changes, else stands at the last Dec 11, 2011 · The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Feb 23, 2005 · You see, on one day every year, the King would put the names of all the prisoners in a hat and draw out 3 names. View full lesson: http://ed. On the other side of the wall is prisoner 4, who cannot see anybody’s hat. Prisoner B can see prisoner C. In a remote prison somewhere in South Mar 16, 2009 · A very nice riddle. Otherwise, they will all be executed. Person 2 sees a red hat on person 3, which eliminates 3 possibilities and leaves 3 possibilities. But now prisoner 3 can reason that Feb 18, 2023 · Prisoner 1 can see the color hat of prisoners 2 and 3. Number 2 sees number 3's hat. npsi ejuh clukc swukuksy mgnot umss hbsbgd eavhvx whvp dmh wijhnm fubqw blrcdd zdufwzl zxuwci