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DNA SortingTime Limit: 1000MSMemory Limit: 10000KTotal Submissions: 63738Accepted: 25165DescriptionOne measure of ``unsortedness'' in a sequence is the number of pairs of entries that are out of order with respect to each other. For instance, in the letter sequence ``DAABEC'', this m 阅读全文
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HumidexTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 10912Accepted: 4071DescriptionAdapted from Wikipedia, the free encyclopediaThe humidex is a measurement used by Canadian meteorologists to reflect the combined effect of heat and humidity. It differs from the heat index used in the Unit 阅读全文
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Dirichlet's Theorem on Arithmetic ProgressionsTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 11334Accepted: 5693DescriptionIf a and d are relatively prime positive integers, the arithmetic sequence beginning with a and increasing by d, i.e., a, a + d, a + 2d, a + 3d, a + 4d, ..., conta 阅读全文
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Sum of Consecutive Prime NumbersTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 13050Accepted: 7255DescriptionSome positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the integ 阅读全文
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Goldbach's ConjectureTime Limit: 1000MSMemory Limit: 65536KTotal Submissions: 28913Accepted: 11072DescriptionIn 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture: Every even number greater than 4 can bewritten as t 阅读全文
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DescriptionAncient Roman empire had a strong government system with various departments, including a secret service department. Important documents were sent between provinces and the capital in encrypted form to prevent eavesdropping. The most popular ciphers in those times were so called substitut 阅读全文
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Integer InquiryTime Limit: 1000MSMemory Limit: 10000KTotal Submissions: 23072Accepted: 8987DescriptionOne of the first users of BIT's new supercomputer was Chip Diller. He extended his exploration of powers of 3 to go from 0 to 333 and he explored taking various sums of those numbers. ``This sup 阅读全文
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Moving TablesTime Limit: 1000MSMemory Limit: 10000KTotal Submissions: 20016Accepted: 6539DescriptionThe famous ACM (Advanced Computer Maker) Company has rented a floor of a building whose shape is in the following figure. The floor has 200 rooms each on the north side and south side alo... 阅读全文