Tom meets a new neighbour, Cheryl, next door to him. During the conversation with Cheryl, Tom asks her: “How many kids do you have”. “Three” replied Cheryl. Tom asked “How old are they?” Cheryl answered:”The product of their ages is 36. The sum of their ages are the same as my house number.” After some time Tom replied “I can’t figure it out. I don’t have enough information”. “My apologies, I forgot to tell you that my youngest child likes strawberry milk” replied Cheryl. Tom figured out their ages after her answer and Cheryl confirmed that he was right. How old are Cheryl’s children?

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Diophantus was a Greek mathematician. Little is known about the life of Diophantus except for an algebraic riddle from around the early sixth century. The riddle states: Here lies Diophantus,’ the wonder behold. Through art algebraic, the stone tells how old: ‘God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father’s life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.’ How many years did Diophantus live based on the riddle?

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Your friend has 100 red marbles, 100 blue marbles and 2 jars. He proposes a game. He fills the jars with the marbles, put the two jars behind his back and tell you to pick one of them at random. You’ll then close your eyes, he’ll hand you the jar you picked, and you’ll pick a random marble from that jar. You win if the marble you pick is blue, and you lose otherwise. To give you the best shot at winning, your friend gives you the two jars before the game starts and says you can move the marbles around however you’d like, as long as all 200 marbles are in one of the 2 jars (that is, you can’t throw any marbles away). How should you move the marbles around to give yourself the best chance of picking a blue marble?

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There is a row of soldiers that is 1km in length and they walk with a constant speed in a straight line, in one direction. All the way at the end walks a messenger. He has to bring a message to the captain walking all the way at the beginning of the row. The messenger starts walking past the soldiers and immediately turns around when arriving at the captain and walks back to the end of the row. When the messenger is back at the end, the whole group of soldiers have traveled a distance of 1 km. The soldiers and captain are walking at the same constant speed. The messenger (walking faster then the soldiers) is also walking a a constant speed. You don’t know anything about time or speed. How far did the messenger travel from the end of the row to the beginning and back?

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On a certain island there are people with assorted eye colors. There are 100 people with blue eyes and 100 people with brown eyes. Since there are no mirrors on this island, no person knows the color of their own eyes. The people on the island are not allowed to talk or communicate with each other in any way. They are also not aware of the number of blue or brown eyed people on the island. For all they know, they could have red eyes too. But they are allowed to observe other people and keep count of the number of people with a certain eye color. There is a rule that the people on the island have to follow – any person who is sure of their eye color has to leave the island immediately. One day, a person comes to the island and announces to the people that he sees someone with blue eyes. Everyone knows that the person only speaks the truth. What do you think happens?

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A friend of mine emptied a box of matches on the table and divided them into three heaps, while we stood around him wondering what he was going to do next. He looked up and said, “Well friends, we have here three uneven heaps. Of course you know that a match box contains altogether 48 matches. This I don’t have to tell you. And I am not going to tell you how many there are in each heap.” “What do you want us to do?” one of the men shouted. “Look well, and think. If I take off as many matches from the first heap as there are in the second and add them to the second, and then take as many from the second as there are in the third and add them to the third, and lastly if I take as many from the third as there are in the first and add them to the first—then the heaps will all have equal number of matches.” As we all stood there puzzled he asked, “Can you tell me how many were there originally in each heap?” Can you?

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There are 1 million closed school lockers in a row, labeled 1 through 1,000,000. You first go through and flip every locker open. Then you go through and flip every other locker (locker 2, 4, 6, etc…). When you’re done, all the even-numbered lockers are closed. You then go through and flip every third locker (3, 6, 9, etc…). “Flipping” mean you open it if it’s closed, and close it if it’s open. For example, as you go through this time, you close locker 3 (because it was still open after the previous run through), but you open locker 6, since you had closed it in the previous run through. Then you go through and flip every fourth locker (4, 8, 12, etc…), then every fifth locker (5, 10, 15, etc…), then every sixth locker (6, 12, 18, etc…) and so on. At the end, you’re going through and flipping every 999,998th locker (which is just locker 999,998), then every 999,999th locker (which is just locker 999,999), and finally, every 1,000,000th locker (which is just locker 1,000,000). At the end of this, is locker 1,000,000 open or closed?

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