Brain Teasers & Puzzles

There is a polynomial and you have access to a function that evaluates that polynomial at a given number. You don’t know the degree of the polynomial, nor do you know any of the coefficients of its terms. However, you are told that all coefficients are nonnegative integers. How many times do you need to call the evaluation function in order to identify the polynomial (that is, to figure out the values of its coefficients)?
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There is a table with a row of 2014 cards. Each card has a red side and a blue side. We’ll say that a card is red if the color on its visible face is red, and analogously for blue. Two players take turns to do the following move: select any 50 consecutive cards where the leftmost card is red, then flip each of those 50 cards (thus, for those 50 cards, turning red cards into blue cards and blue cards into red cards). Both players look at the cards from the same side of the table, so “leftmost” means the same to both of the players (that is, you can think of one of the ends of the table as being designated as the left end). When it is a player’s turn, if that player cannot make a move (that is, if there is no way to select 50 consecutive cards the leftmost one of which is red), then that player loses and the other player wins. If you are one of the players and all cards are initially red, can you be sure to win, and if so, do you want to be the player who goes first or second?
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Two arbitrary rectangles are placed to form an “L”. That is, the lower lefthand corner of the two rectangles share the same point. (What I’m trying to say is that there’s an “L” whose “I” and “_” parts have arbitrary widths and heights.) Using only a (pen and a) straightedge (that is, no measuring device and no compass), figure out a way to, with a single straight cut, divide the “L” into two pieces of equal area.
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A homicide team enters a crime scene where a dead body of a fat old man lies there on the floor with blood oozing out of his head. The victim is holding a gun and a tape recorder lies there by his side. One of the detective picks up the recorder and plays it “I am tired of this life and hence I have decided to relieve myself from the worldly pains”. A gunshot follows the message.
The teams starts investigating a murder investigation.
Why?
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You had an infinite supply of water and a 5 ml and 3 ml gallons.
How would you measure exactly 4 ml in least number of steps ?
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A guy claims to do the following thing. He puts a coin in a glass bottle. Then, he shuts the mouth of the bottle with the help of a cork. Now he manages to remove the coin out from the bottle without taking out the cork or breaking the glass bottle.
Do you know how he can do it?
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Complete the pyramid my replacing ? with the correct number.
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
? ? ? ? ? ?
? ? ? ? ? ? ? ?View SolutionSubmit Solution 1,300.1K views
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A conference room contains three separate wallmounted spotlights – right, left and front of stage. Each is controlled by its own onoff switch. These three switches are numbered 1, 2 and 3, but they are in a backroom which has no sight of the the spotlights or the conference room (and there are no reflections or shadows or mirrors, and you are alone). How do you identify each switch correctly – right, left, front – if you can only enter the backroom once?
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