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A cube of side 4cm is painted with colors red,blue,green in such a way that opposite sides are painted in the same colour . this cube is now cut into 64 cubes of equal size .then 1) how many have atleast two sides painted in different colours. 2) how many cubes have only one side painted. 3) how many cubes have no side painted 4) how many have exactly one side not painted.

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If 12 distinct points are placed on the circumference of a circle and all the chords connecting these points are drawn. What is the largest number of points of intersection for these chords?

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Let D be the set of all points in the real plane such that x + y <= 1, where x (respectively y) denotes the absolute value of x (respectively y). Prove that amongst every 5 points in D, there exist two points whose distance from one another is at most 1.

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A bus run at 100 km/hr top speed. It can carry a maximum of 6 persons. If speed of bus decreases in fixed proportion with increase in number of person, find speed when three person are traveling in bus?

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There is a whole number n for which the following holds: if you put a 4 at the end of n, and multiply the number you get in that way by 4, the result is equal to the number you get if you put a 4 in front of n. In other words, we are looking for the number you can put on the dots in the following equation: 4... = 4 ?...4 Which number must be put on the dots to get a correct equation?

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The fraction EVE/DID = 0,TALKTALKTALKTALK... is a normal fraction that can also be written as a recurring decimal. Which fraction is this (equal letters are equal ciphers)?

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A cable, 16 meters in length, hangs between two pillars that are both 15 meters high. The ends of the cable are attached to the tops of the pillars. At its lowest point, the cable hangs 7 meters above the ground. How far are the two pillars apart?

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The legendary king Midas possessed a huge amount of gold. He hid this treasure carefully: in a building consisting of a number of rooms. In each room there were a number of boxes; this number was equal to the number of rooms in the building. Each box contained a number of golden coins that equaled the number of boxes per room. When the king died, one box was given to the royal barber. The remainder of the coins had to be divided fairly between his six sons. Is a fair division possible in all situations?

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This is a most unusual paragraph. How quickly can you find out what is so unusual about it? It looks so ordinary that you would think that nothing is wrong with it at all, and, in fact, nothing is. But it is unusual. Why? If you study it and think about it, you may find out, but I am not going to assist you in any way. You must do it without any hints or coaching. No doubt, if you work at it for a bit, it will dawn on you. Who knows? Go to work and try your skill. Good luck! What is unusual about the above paragraph?

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Here is a sequence of numbers: 1 11 21 1211 111221 It seems to be a strange sequence, but yet there is a system behind it... What is the next term in this sequence?

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Below are a number of statements: 1. Precisely one of these statements is untrue. 2. Precisely two of these statements are untrue. 3. Precisely three of these statements are untrue. 4. Precisely four of these statements are untrue. 5. Precisely five of these statements are untrue. 6. Precisely six of these statements are untrue. 7. Precisely seven of these statements are untrue. 8. Precisely eight of these statements are untrue. 9. Precisely nine of these statements are untrue. 10. Precisely ten of these statements are untrue. Which of these statements is true?

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Three salesmen went into a hotel to rent a room. The manager stated that he had only one room left, but all three could use it for $30.00 for the night. The three salesmen gave him $10.00 each and went up to their room. Later, the manager decided that he had charged the salesmen too much so he called the bellhop over, gave him five onedollar bills, and said: 'Take this $5.00 up to the salesmen and tell them I had charged them too much for the room'. On the way up, the bellhop knew that he could not divide the five onedollar bills equally so he put two of the onedollar bills in his pocket and returned one onedollar bill to each of the salesmen. This means that each salesman paid $9.00 for the room. The bellhop kept $2.00. Three times nine is 27 plus two is 29....... What happened to the extra dollar?

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A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?

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Joyce has bought ten trees for her garden. She wants to plant these trees in five rows, with four trees in each row. The Question :How must Joyce plant the trees?

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Using the ciphers 1 up to 9, three numbers (of three ciphers each) can be formed, such that the second number is twice the first number, and the third number is three times the first number. Which are these three numbers?

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The poor have it, the rich want it, but if you eat it you will die. What is this?

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In the Tour de France, what is the position of a rider, after he passes the second placed rider?

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In Miss Miranda's class are eleven children. Miss Miranda has a bowl with eleven apples. Miss Miranda wants to divide the eleven apples among the children of her class, in such a way that each child in the end has an apple and one apple remains in the bowl. Can you help Miss Miranda?

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Hans is standing behind Gerrie and at the same time Gerrie is standing behind Hans. How is this possible

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Of all the numbers whose literal representations in capital letters consists only of straight line segments (for example, FIVE), only one number has a value equal to the number of segments used to write it. Which number has this property?

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