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