# Euler problems/71 to 80

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[[Category:Programming exercise spoilers]] | [[Category:Programming exercise spoilers]] | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=71 Problem 71] == |

Listing reduced proper fractions in ascending order of size. | Listing reduced proper fractions in ascending order of size. | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=72 Problem 72] == |

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? | How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=73 Problem 73] == |

How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions? | How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions? | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=74 Problem 74] == |

Determine the number of factorial chains that contain exactly sixty non-repeating terms. | Determine the number of factorial chains that contain exactly sixty non-repeating terms. | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=75 Problem 75] == |

Find the number of different lengths of wire can that can form a right angle triangle in only one way. | Find the number of different lengths of wire can that can form a right angle triangle in only one way. | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=76 Problem 76] == |

How many different ways can one hundred be written as a sum of at least two positive integers? | How many different ways can one hundred be written as a sum of at least two positive integers? | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=77 Problem 77] == |

What is the first value which can be written as the sum of primes in over five thousand different ways? | What is the first value which can be written as the sum of primes in over five thousand different ways? | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=78 Problem 78] == |

Investigating the number of ways in which coins can be separated into piles. | Investigating the number of ways in which coins can be separated into piles. | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=79 Problem 79] == |

By analysing a user's login attempts, can you determine the secret numeric passcode? | By analysing a user's login attempts, can you determine the secret numeric passcode? | ||

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</haskell> | </haskell> | ||

− | == [http://projecteuler.net/index.php?section= | + | == [http://projecteuler.net/index.php?section=view&id=80 Problem 80] == |

Calculating the digital sum of the decimal digits of irrational square roots. | Calculating the digital sum of the decimal digits of irrational square roots. | ||

## Revision as of 13:54, 20 July 2007

## Contents |

## 1 Problem 71

Listing reduced proper fractions in ascending order of size.

Solution:

problem_71 = undefined

## 2 Problem 72

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

Solution:

problem_72 = undefined

## 3 Problem 73

How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions?

Solution:

problem_73 = undefined

## 4 Problem 74

Determine the number of factorial chains that contain exactly sixty non-repeating terms.

Solution:

problem_74 = undefined

## 5 Problem 75

Find the number of different lengths of wire can that can form a right angle triangle in only one way.

Solution: This is only slightly harder than problem 39. The search condition is simpler but the search space is larger.

problem_75 = length . filter ((== 1) . length) $ group perims where perims = sort [scale*p | p <- pTriples, scale <- [1..10^6 `div` p]] pTriples = [p | n <- [1..1000], m <- [n+1..1000], even n || even m, gcd n m == 1, let a = m^2 - n^2, let b = 2*m*n, let c = m^2 + n^2, let p = a + b + c, p <= 10^6]

## 6 Problem 76

How many different ways can one hundred be written as a sum of at least two positive integers?

Solution:

problem_76 = undefined

## 7 Problem 77

What is the first value which can be written as the sum of primes in over five thousand different ways?

Solution:

problem_77 = undefined

## 8 Problem 78

Investigating the number of ways in which coins can be separated into piles.

Solution:

problem_78 = undefined

## 9 Problem 79

By analysing a user's login attempts, can you determine the secret numeric passcode?

Solution:

problem_79 = undefined

## 10 Problem 80

Calculating the digital sum of the decimal digits of irrational square roots.

Solution:

problem_80 = undefined