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Humble NumbersFor a given set of K prime numbers S = {p1, p2, ..., pK}, consider the set of all numbers whose prime factors are a subset of S. This set contains, for example, p1, p1p2, p1p1, and p1p2p3(among others). This is the set of `humble numbers' for the input set S. Note: The number 1 is 阅读全文
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Farmer John is considering purchasing a new herd of cows. In this new herd, each mother cow gives birth to two children. The relationships among the cows can easily be represented by one or more binary trees with a total of N (3 <= N < 200) nodes. The trees have these properties:The degree of 阅读全文
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To brighten up the gala dinner of the IOI'98 we have a set of N (10 <= N <= 100) colored lamps numbered from 1 to N.The lamps are connected to four buttons:Button 1: When this button is pressed, all the lamps change their state: those that are ON are turned OFF and those that are OFF are t 阅读全文
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Runaround numbers are integers with unique digits, none of which is zero (e.g., 81362) that also have an interesting property, exemplified by this demonstration:If you start at the left digit (8 in our number) and count that number of digits to the right (wrapping back to the first digit when no dig 阅读全文
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Barn RepairIt was a dark and stormy night that ripped the roof and gates off the stalls that hold Farmer John's cows. Happily, many of the cows were on vacation, so the barn was not completely full.The cows spend the night in stalls that are arranged adjacent to each other in a long line. Some s 阅读全文
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TransformationsA square pattern of size N x N (1 <= N <= 10) black and white square tiles is transformed into another square pattern. Write a program that will recognize the minimum transformation that has been applied to the original pattern given the following list of possible transformation 阅读全文
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Milking CowsThree farmers rise at 5 am each morning and head for the barn to milk three cows. The first farmer begins milking his cow at time 300 (measured in seconds after 5 am) and ends at time 1000. The second farmer begins at time 700 and ends at time 1200. The third farmer begins at time 1500 a 阅读全文