Euler problems/51 to 60
Find the smallest prime which, by changing the same part of the number, can form eight different primes.
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Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order.
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How many values of C(n,r), for 1 ≤ n ≤ 100, exceed one-million?
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How many hands did player one win in the game of poker?
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How many Lychrel numbers are there below ten-thousand?
problem_55 = length $ filter isLychrel [1..9999] where isLychrel n = all notPalindrome (take 50 (tail (iterate revadd n))) notPalindrome s = (show s) /= reverse (show s) revadd n = n + rev n where rev n = read (reverse (show n))
Considering natural numbers of the form, ab, finding the maximum digital sum.
problem_56 = maximum [dsum (a^b) | a <- [1..99], b <-[1..99]] where dsum 0 = 0 dsum n = let ( d, m ) = n `divMod` 10 in m + ( dsum d )
Investigate the expansion of the continued fraction for the square root of two.
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Investigate the number of primes that lie on the diagonals of the spiral grid.
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Using a brute force attack, can you decrypt the cipher using XOR encryption?
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10 Problem 60
Find a set of five primes for which any two primes concatenate to produce another prime.
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