Euler problems/51 to 60

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Revision as of 07:24, 30 March 2007 by Quale (talk | contribs) ([ Problem 56]: a solution)

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Problem 51

Find the smallest prime which, by changing the same part of the number, can form eight different primes.


problem_51 = undefined

Problem 52

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order.


problem_52 = undefined

Problem 53

How many values of C(n,r), for 1 ≤ n ≤ 100, exceed one-million?


problem_53 = undefined

Problem 54

How many hands did player one win in the game of poker?


problem_54 = undefined

Problem 55

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))

Problem 56

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 )

Problem 57

Investigate the expansion of the continued fraction for the square root of two.


problem_57 = undefined

Problem 58

Investigate the number of primes that lie on the diagonals of the spiral grid.


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Problem 59

Using a brute force attack, can you decrypt the cipher using XOR encryption?


problem_59 = undefined

Problem 60

Find a set of five primes for which any two primes concatenate to produce another prime.


problem_60 = undefined