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Problem 63 Powerful digit counts

Problem 63: Powerful digit counts

https://projecteuler.net/problem=63

The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit nu[……]

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Problem 62 Cubic permutations

Problem 62: Cubic permutations

https://projecteuler.net/problem=62

The cube, 41063625 (3453), can be permuted to produce two other cubes: 56623104 ([……]

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Problem 61 Cyclical figurate numbers

Problem 61: Cyclical figurate numbers

https://projecteuler.net/problem=61

Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers[……]

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Problem 60 Prime pair sets

Problem 60: Prime pair sets

https://projecteuler.net/problem=60

The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and co[……]

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Problem 59 XOR decryption

Problem 59: XOR decryption

https://projecteuler.net/problem=59

Each character on a computer is assigned a unique code and the preferred standard is[……]

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Problem 58 Spiral primes

Problem 58: Spiral primes

https://projecteuler.net/problem=58

Starting with 1 and spiralling anticlockwise in the following way, a square spiral wit[……]

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Problem 57: Square root convergents

Problem 57: Square root convergents

https://projecteuler.net/problem=57

分析

每次扩展,相当于将 1/2 替换为 1/(2+1/2),所以

第 1 次扩展结果: fraction = 1 + 1/2
第 2 次扩展结果:[......]

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Problem 56 Powerful digit sum

Problem 56: Powerful digit sum

https://projecteuler.net/problem=56

A googol (10100) is a massive number: one followed by one-hundred zeros; 100100 i[……]

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Problem 55 Lychrel numbers

Problem 55: Lychrel numbers

https://projecteuler.net/problem=55

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers[……]

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Problem 54 Poker hands

Problem 54: Poker hands

https://projecteuler.net/problem=54

download poker.txt

分析

扑克游戏

扑克游戏中,一手牌包括5张卡牌,并且等级(rank)从低到高排序如下:

Problem 53 Combinatoric selections

Problem 53: Combinatoric selections

https://projecteuler.net/problem=53

分析

组合 C(n,r) 表示从 n 个数中选择 r 个数选择方案的总数。 当 1 ≤ n ≤ 1000时, 统计有多少个 C(n,r) 的值超过了[……]

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Problem 52 Permuted multiples

Problem 52: Permuted multiples

https://projecteuler.net/problem=52

It can be seen that the number, 125874, and its double, 251748, contain exactly t[……]

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Problem 51 Prime digit replacements

Problem 51: Prime digit replacements

https://projecteuler.net/problem=51

By replacing the 1st digit of the 2-digit number *3, it turns out that six[……]

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Problem 50 Consecutive prime sum

Problem 50: Consecutive prime sum

https://projecteuler.net/problem=50

The prime 41, can be written as the sum of six consecutive primes:

41 = 2 + 3[……]

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Problem 44 Pentagon numbers

Problem 44: Pentagon numbers

https://projecteuler.net/problem=44

Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentag[……]

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