Difference between revisions of "Euler problems/71 to 80"
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[[Category:Programming exercise spoilers]] |
[[Category:Programming exercise spoilers]] |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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> |
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− | == [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. |
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Revision as of 13:54, 20 July 2007
Problem 71
Listing reduced proper fractions in ascending order of size.
Solution:
problem_71 = undefined
Problem 72
How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?
Solution:
problem_72 = undefined
Problem 73
How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions?
Solution:
problem_73 = undefined
Problem 74
Determine the number of factorial chains that contain exactly sixty non-repeating terms.
Solution:
problem_74 = undefined
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]
Problem 76
How many different ways can one hundred be written as a sum of at least two positive integers?
Solution:
problem_76 = undefined
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
Problem 78
Investigating the number of ways in which coins can be separated into piles.
Solution:
problem_78 = undefined
Problem 79
By analysing a user's login attempts, can you determine the secret numeric passcode?
Solution:
problem_79 = undefined
Problem 80
Calculating the digital sum of the decimal digits of irrational square roots.
Solution:
problem_80 = undefined