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Euler problems/71 to 80

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[[Category:Programming exercise spoilers]]
 
[[Category:Programming exercise spoilers]]
== [http://projecteuler.net/index.php?section=problems&id=71 Problem 71] ==
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== [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=problems&id=72 Problem 72] ==
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== [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=problems&id=73 Problem 73] ==
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== [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=problems&id=74 Problem 74] ==
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== [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=problems&id=75 Problem 75] ==
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== [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=problems&id=76 Problem 76] ==
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== [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=problems&id=77 Problem 77] ==
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== [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=problems&id=78 Problem 78] ==
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== [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=problems&id=79 Problem 79] ==
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== [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=problems&id=80 Problem 80] ==
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== [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