Three Inch Origami
What is the minimum number of folds you need in order to create a 3-inch measurement from an 8.5×11 inches paper?
What is the minimum number of folds you need in order to create a 3-inch measurement from an 8.5×11 inches paper?
Nine pirates have captured a treasure chest. In order to protect it, they decide to lock it using multiple locks and distribute several keys for each of these locks among them, so that the chest can be opened only by a majority of the pirates. What is the minimum number of keys each of the pirates should get?
Three friends, Adam, Bob, and Charlie are buried in the sand up to their necks, all facing West. Charlie can see both Adam and Bom, Bom can see only Adam, and Adam cannot see anyone. Black and white hats are placed on their heads. The three friends are told that there is at least one hat from each color, and then they are asked whether anyone can guess the color of their own hat.
After a few minutes, one of them answers. Who is that?
A hundred fish are swimming along a stream at different velocities. If one fish catches up to another fish, it eats it and continues swimming. What is the expected number of fish that will survive?
There is a perfectly spherical apple with a radius 50mm. A worm has entered the apple, made a tunnel of length 99mm through it and left. Prove that we can slice the apple in two pieces through the center, so that one of them is untouched by the worm.
Sarah lives in the UK. Which of these statements is least likely:
Bobby and Garry are playing chess. If Garry is playing with the black figures and agrees to mirror every move Bobby makes, what is the minimum number of moves in which Bobby can mate his opponent?
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