There are 1000 bankers in a room--500 of which have brown feathered hats and 500 of which have black feathered hats. They are forbidden to communicate with one another or take their hats off. There are no mirrors or reflecting surfaces in the room. Because of an unspoken rule that all of the bankers understand and abide by, if at any time during the course of the day someone discovers the color of the feather in his hat, he or she must leave the room at midnight that evening. Every person in the room is a perfect logician, can see the color of every other banker's feather (except his or her own), and knows the number of bankers in the room at any given time.One day (when all 1000 of the bankers are in the room), Ben Bernanke who wears a white feather, walks into the room and proclaims, without looking at any specific banker, "I see a banker with a brown feather," and then sits down in a corner, refusing to answer any other questions and abiding by the same rules as every other banker in the room.The question is when, if ever, do any of the bankers leave the room? What color feathers are they wearing? How many leave?
(a) I have two buckets - one filled with Sprite and the other filled with Coke. The volumes of Sprite and Coke are equal. Using a standard Solo cup, I scoop one cup-full of Sprite out and pour it into the Coke bucket. I mix the Sprite-Coke mixture until it is of equal composition throughout the bucket. Using the same Solo cup, I scoop one cup-full of the Sprite-Coke mixture out and pour it into the pure Sprite bucket. I mix that mixture until it is of equal composition throughout the bucket. Which is greater: the concentration of Sprite in the Coke bucket or the concentration of Coke in the Sprite bucket?
V. FINANCE KNOWLEDGE(b) I have a tap, a drain, a 3 gallon bucket, and a 5 gallon bucket. I can get unlimited water from the tap and pour unlimited water down the drain. Using only these items, how can I measure 4 gallons of water?(c) I have a string and a lighter. The string burns from one end to the other in 30 minutes but not necessarily at a constant rate (i.e., the first half might burn in 5 minutes while the second half burns in 25 minutes). How do you measure 15 minutes time?
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