# Difference between revisions of "Euler problems/71 to 80"

BrettGiles (talk | contribs) m (EulerProblems/71 to 80 moved to Euler problems/71 to 80) |
(→[http://projecteuler.net/index.php?section=problems&id=75 Problem 75]: a solution) |
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Line 36: | Line 36: | ||

Solution: |
Solution: |
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<haskell> |
<haskell> |
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− | problem_75 = undefined |
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+ | problem_75 = length . filter ((== 1) . length) $ perims |
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+ | where perims = group $ sort [scale*p | p <- pTriples, scale <- [1..10^6 `div` p]] |
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+ | pTriples = [p | |
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+ | n <- [1..1000], |
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+ | m <- [n+1..1000], |
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+ | even n || even m, |
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+ | gcd n m == 1, |
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+ | let a = m^2 - n^2, |
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+ | let b = 2*m*n, |
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+ | let c = m^2 + n^2, |
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+ | let p = a + b + c, |
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+ | p <= 10^6] |
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</haskell> |
</haskell> |
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## Revision as of 08:35, 30 March 2007

## Contents

## 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:

```
problem_75 = length . filter ((== 1) . length) $ perims
where perims = group $ 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
```