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In the 20×20 grid below, four numbers along a diagonal line have been marked in red. 阅读全文
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The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below two million. 阅读全文
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A Pythagorean triplet is a set of three natural numbers, a b c, for which, a2 + b2 = c2For example, 32 + 42 = 9 + 16 = 25 = 52.There exists exactly one Pythagorean triplet for which a + b + c = 1000.Find the product abc.寻找和为1000毕达哥拉斯三元数组，求它们的积由于a b c，我们容易得到a的范围a < 1000/(1+1+1.414); 估算有 a < 300 阅读全文
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Find the greatest product of five consecutive digits in the 1000-digit number.731671765313306249192251196744265747423553491949349698352031277450632623957831801698480186947885184385861560789112949495459501737958331952853208805511125406987471585238630507156932909632952274430435576689664895044524452316 阅读全文
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By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.What is the 10001st prime number?求第10001个素数。求素数有很多种方法最直接的方法就是看这个数能不能整除2～sqrt（该数）；而查表法能做更少的运算，如果一个数不能被小于它的素数整除的话，那么该数就是素数。如23不能被2，3，5，7，11，13，17，19整除。更进一步，一个数不能被2～sqrt（该数）中的素数整除的话，那么该数就是素数。所以，23只要不能被2， 阅读全文
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The sum of the squares of the first ten natural numbers is,12 + 22 + ... + 102 = 385The square of the sum of the first ten natural numbers is,(1 + 2 + ... + 10)2 = 552 = 3025Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 阅读全文
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2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?题目的要求就是求1，2，3 ··· ··· 20的最小公倍数我们可惜先求1，2的最小公倍数2再求2，3的最小公 阅读全文