摘要：Problem Description The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will 阅读全文

摘要：Problem Description Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. 37 36 35 34 33 32 3138 17 16 15 14 13 3039 18 5 4 3 12 2940 19 6 1 ... 阅读全文

摘要：Problem Description Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange). For example, uppercase A = 65, aste... 阅读全文

摘要：Problem Description It is possible to show that the square root of two can be expressed as an infinite continued fraction. sqrt(2) = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213... By expanding this f... 阅读全文

摘要：Problem Description A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the... 阅读全文

摘要：Problem Description If we take 47, reverse and add, 47 + 74 = 121, which is palindromic. Not all numbers produce palindromes so quickly. For example, 349 + 943 = 1292,1292 + 2921 = 42134213 + 3124 = 7... 阅读全文

摘要：Problem Description By replacing the 1st digit of *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime. By replacing the 3rd and 4th digits of 56**3 with t... 阅读全文

摘要：Problem Description In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: High Card: Highest value card. One Pair: Two cards of the same... 阅读全文

摘要：Problem DescriptionThere are exactly ten ways of selecting three from five, 12345:123, 124, 125, 134, 135, 145, 234, 235, 245, and 345In combinatorics, we use the notation, 5C3= 10.In general,nCr =n!r!(n-r)!,where r<=n, n! = n*(n-1)…*3*2*1, and 0! = 1.It is not until n = 23, that a value exceeds 阅读全文

摘要：Problem Description It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order. Find the smallest positive integer, x, such that 2x, 3x, ... 阅读全文

摘要：Problem Description The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13 This is the longest sum of consecutive primes that adds to a prime below one-hundred... 阅读全文

摘要：Problem DescriptionThe arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.There are no arithmetic sequences made up of three 1-, 2-, 阅读全文

摘要：Problem Description The series, 11 + 22 + 33 + ... + 1010 = 10405071317. Find the last ten digits of the series, 11 + 22 + 33 + ... + 10001000. Python This problem is so easy to python, because pyt... 阅读全文