1 Can the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 be arranged on a circle in such a manner that the difference between any two adjacent numbers is either 3 or 4 or 5?
2 Two hundred soldiers form a rectangular array with ten soldiers in each line and twenty soldiers in each file. From each line the smallest soldier is chosen, after which among the twenty soldiers thus taken, the tallest one is chosen. Then from each file of the original array the tallest soldier is chosen, after which among the ten soldiers thus taken the smallest one is chosen. Which of the soldiers, that is the smallest among the tallest and the tallest among the smallest is taller? (provided they are different persons )
3 Can a knight move from the left lower corner of the chessboard to the right upper corner passing through each of the squares of the chessboard exactly once?
4 Three missionaries & three cannibals decide to cross a river. The difficulty is that they can't swim. But the advantage is that they have a small boat with an outboard motor, which can carry only 2 persons at a time. Each of the missionaries can operate the outboard motor, but only one of the cannibals can do so. If, by chance, at any of the banks, the number of cannibals is greater than the number of the missionaries, then the missionaries will get killed & eaten by the cannibals. How can all of them cross the river so that all six of them are safely delivered on the other side of river?
5 A king had 7 daughters. He had some number of pearls, which he wanted to divide equally among his daughters. One night one of his daughters got up and went to steal the pearls. But, while she was stealing, the second daughter got up and both of them decided to share the pearls equally among themselves and found one pearl extra while doing so. By the time the two daughters could steal the pearls the third daughter got up and the three of them decided to share the pearls equally among themselves, in doing so they once again found one pearl extra. Similarly the 4th, 5th, 6th daughters also got up and found one pearl extra while dividing it into 4, 5 and 6 parts respectively. After this the 7th daughter got up and the seven daughters decided to divide the pearls equally among themselves and found that the pearls were equally divisible. What is minimum number of pearls the king must have had for such a situation to be possible?
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