text: # Euler problems/51 to 60
  
  (Difference between revisions)
  
  ## 1 Problem 51
  
  Find the smallest prime which, by changing the same part of the number, can form eight different primes.
  
  Solution:
  
  `problem_51 = undefined`
  
  ## 2 Problem 52
  
  Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order.
  
  Solution:
  
  `problem_52 = undefined`
  
  ## 3 Problem 53
  
  How many values of C(n,r), for 1 ≤ n ≤ 100, exceed one-million?
  
  Solution:
  
  `problem_53 = undefined`
  
  ## 4 Problem 54
  
  How many hands did player one win in the game of poker?
  
  Solution:
  
  `problem_54 = undefined`
  
  ## 5 Problem 55
  
  How many Lychrel numbers are there below ten-thousand?
  
  Solution:
  
  ```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))```
  
  ## 6 Problem 56
  
  Considering natural numbers of the form, ab, finding the maximum digital sum.
  
  Solution:
  
  ```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 )```
  
  ## 7 Problem 57
  
  Investigate the expansion of the continued fraction for the square root of two.
  
  Solution:
  
  `problem_57 = undefined`
  
  ## 8 Problem 58
  
  Investigate the number of primes that lie on the diagonals of the spiral grid.
  
  Solution:
  
  `problem_58 = undefined`
  
  ## 9 Problem 59
  
  Using a brute force attack, can you decrypt the cipher using XOR encryption?
  
  Solution:
  
  `problem_59 = undefined`
  
  ## 10 Problem 60
  
  Find a set of five primes for which any two primes concatenate to produce another prime.
  
  Solution:
  
  `problem_60 = undefined`