# Euler problems/181 to 190

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< Euler problems(Difference between revisions)

Robinrobin (Talk | contribs) ((183) If we must have a solution here, let's at least have a decent one.) |
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− | + | -- Does the decimal expansion of p/q terminate? | |

− | + | terminating p q = 1 == reduce [2,5] (q `div` gcd p q) | |

− | + | where reduce [] n = n | |

− | + | reduce (x:xs) n | n `mod` x == 0 = reduce (x:xs) (n `div` x) | |

− | + | | otherwise = reduce xs n | |

− | + | ||

− | + | -- The expression (round $ fromIntegral n / e) computes the integer k | |

− | + | -- for which (n/k)^k is at a maximum. | |

− | n ` | + | answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n |

− | + | | n <- [5 .. 10^4]] | |

− | + | where e = exp 1 | |

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− | + | main = print answer | |

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</haskell> | </haskell> |

## Revision as of 20:27, 24 February 2008

## 1 Problem 181

Investigating in how many ways objects of two different colours can be grouped.

Solution: This was my code, published here without my permission nor any attribution, shame on whoever put it here. Daniel.is.fischer

## 2 Problem 182

RSA encryption.

Solution:

fun a1 b1 = sum [ e | e <- [2..a*b-1], gcd e (a*b) == 1, gcd (e-1) a == 2, gcd (e-1) b == 2 ] where a=a1-1 b=b1-1 problem_182=fun 1009 3643

## 3 Problem 183

Maximum product of parts.

Solution:

-- Does the decimal expansion of p/q terminate? terminating p q = 1 == reduce [2,5] (q `div` gcd p q) where reduce [] n = n reduce (x:xs) n | n `mod` x == 0 = reduce (x:xs) (n `div` x) | otherwise = reduce xs n -- The expression (round $ fromIntegral n / e) computes the integer k -- for which (n/k)^k is at a maximum. answer = sum [if terminating n (round $ fromIntegral n / e) then -n else n | n <- [5 .. 10^4]] where e = exp 1 main = print answer