Brain Teasers & Puzzles
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A driver, driving a black car with no headlights inside a black tunnel, and he doesn’t meet with an accident. How is it possible?
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One fine day, Mr. Puzzle and Mr. Fry were playing cards, but suddenly power went off and they were getting bored. So Mr. Puzzle randomly inverted position of 15 cards out of 52 cards(and shuffled it) and asked Mr. Fry to divide the card in two pile with equal number of inverted cards(number of cards in each pile need not be equal).
It was very dark in the room and Mr. Fry could not see the cards, after thinking a bit Mr. Fry divided the cards in two piles and quite surprisingly on counting number of inverted cards in both the piles were equal.
What do you think Mr. Fry must have done?
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100 persons are standing in line, each facing the same way. Each person is wearing a hat, either red or blue, but the hat color is not known to the person wearing the hat. In fact, a person knows the hat color only of those persons standing ahead of him in line.
Starting from the back of the line (that is, with the person who can see the hat colors of all of other 99 persons), in order, and ending with the person at the head of the line (that is, with the person who can see the hat color of no one), each person exclaims either “red” or “blue”. These exclamations can be heard by all. Once everyone has spoken, a score is calculated, equal to the number of persons whose exclamation accurately describes their own hat color.
What strategy should the 100 persons use in order to get as high a score as possible, regardless of how the hat colors are assigned? (That is, what strategy achieves the best worst-case score?)
For example, if everyone exclaims “red”, the worst-case score is 0. If the first 99 persons exclaim the color of the hat of the person at the head of the line and the person at the head of the line then exclaims the color he has heard, the worst-case score is 1. If every other person exclaims the hat color of the person immediate in front and that person then repeats the color he has just heard, then the worst-case score is 50. Can you do better?
Hint: Instead of using just red and blue as the possible hat colors and exclamations, use N different colors.
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- 1,449.7K views
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- 1,448.3K views
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Can you find out the number of squares in the given picture?
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Would you believe that the colors of squares A and B are the same? They are!Use your fingers or a piece of paper with holes cut in it to block out the rest of the picture and you will see that they are. [OR look at answer posted below]View SolutionSubmit Solution
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