Euler problems/21 to 30

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Problem 21

Evaluate the sum of all amicable pairs under 10000.


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Problem 22

What is the total of all the name scores in the file of first names?


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Problem 23

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.


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Problem 24

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?


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Problem 25

What is the first term in the Fibonacci sequence to contain 1000 digits?


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Problem 26

Find the value of d < 1000 for which 1/d contains the longest recurring cycle.


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Problem 27

Find a quadratic formula that produces the maximum number of primes for consecutive values of n.


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Problem 28

What is the sum of both diagonals in a 1001 by 1001 spiral?


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Problem 29

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?


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Problem 30

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.


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