| Job Interview (Logic Brainteaser Puzzle) | | | | is red, then clearly this is the box containing red balls. If |
| An employer was very anxious to find the most | | | | white, then white. Since we know that the boxes are |
| intelligent of the three men who had applied for a job. | | | | all incorrectly labeled it is now sufficient to switch the |
| So he told them: ‘here are five conical hats. Three | | | | two remaining labels. |
| are white and two are black. I shall place a hat on | | | | The Local Bus |
| each of your heads. When you turn around, you will be | | | | The local minibus that runs from our village to the |
| able to see the others’ hats but not your own. The | | | | nearest town has the following seating regulations: |
| first one to tell me the color of his own hat will get the | | | | Maximum Capacity: |
| job.’ He then placed a white hat on each man’s | | | | Sitting: 8 adults or 12 children |
| head. When the three men turned to face each other | | | | Standing: 2 adults or 4 children |
| there was a long silence. Then, suddenly, one of the | | | | As the last bus drew up at one of the stops on |
| candidates said, ‘Mine is white.’ | | | | Saturday evening there were six adults who wanted |
| How did he know? | | | | to get on. But there were already seven children in the |
| Clue: There are three possible combinations: two men | | | | bus. How many of the adults would be able to get on |
| had black hats and one a white one (this must be | | | | the bus if the regulations were observed? |
| excluded because if one man had seen two black | | | | Clue: If 12 children can sit in the same space as eight |
| hats, he would immediately have known his was | | | | adults, how much room would three children take up? |
| white); two had white hats and one had a black one; all | | | | Answer: No problem! If 12 children can sit in the same |
| three had white hats. | | | | space as eight adults then three children could sit in the |
| The secret is to work out the color of one’s own | | | | same space for two adults. This meant that if four |
| hat from what the other people must able to see. | | | | children stood up and three remained seated, there |
| Answer: He could see two white hats. Therefore he | | | | would still be room for the six adults to sit down. So |
| might have had on either a white or a black hat. He | | | | everyone was able to get on. |
| then reasoned like this: Suppose my hat is black. If it is, | | | | The Cheating Runners |
| my two rivals A and B can each see a black hat and | | | | When Alex, Brian and Chris finished their race they |
| a white hat. One of them (A) might then work out that | | | | were feeling very tired. It had been raining very heavily, |
| his own hat could not be black because, if it were, B | | | | so heavily in fact that the judges were unable to see |
| would see two black hats and would know that his | | | | who came in first, who second and who third. When |
| own hat must therefore be white. B says nothing | | | | he asked the three men, they each made two |
| however. A might therefore conclude, if my hat is | | | | statements. One man lied in both his statements. The |
| black, then his own hat must be white. But since he | | | | other two told the truth. This is what they said: |
| does not come to this conclusion, then my assumption | | | | Alex said, ‘I came in first, Chris was last.’ |
| that my hat is black must be false. Therefore my hat | | | | Brian said, ’Alex wasn’t first. Chris came in |
| must be white. | | | | second.’ |
| Predicting the Color | | | | Chris said, ‘I was before Alex. Brian wasn’t |
| There are three boxes labeled ‘red balls’, | | | | second.’ |
| ‘White balls’ and ‘red and white balls’. | | | | So what was the order in which they crossed the |
| Each of the labels is incorrect. You are allowed to take | | | | finishing line? |
| one ball only from each box. How can you label each | | | | Clue: What Alex and Brian say about Chris disagrees. |
| box correctly? | | | | Therefore one of them must be lying. |
| (Of course, you are not allowed to look inside!) | | | | Answer: Alex and Brian say different things about |
| Clue: It will be sufficient to correctly identify one box. | | | | Chris. Therefore one of them is lying and Chris must |
| We know that all the boxes are incorrectly labeled. | | | | be telling the truth. Since Chris says he was before |
| Once one box has been correctly identified, all we | | | | Alex, it is obvious that Alex is lying about coming first. |
| need to do is to switch the labels on the other two | | | | Therefore the real order must have been Brian (who |
| boxes. | | | | wasn’t second, according to Chris who told the |
| Answer: The first thing to do is to take a ball from the | | | | truth), then Chris (Because Brian said so, and he also |
| box incorrectly labeled ‘red and white balls’. If it | | | | was telling the truth)-finally Alex. |