# Euler problems/81 to 90

### From HaskellWiki

m (Corrected the links to Project Euler) |
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Line 53: | Line 53: | ||

Solution: | Solution: | ||

<haskell> | <haskell> | ||

− | problem_87 = | + | import List |

+ | |||

+ | problem_87 = length expressible | ||

+ | where limit = 50000000 | ||

+ | squares = takeWhile (<limit) (map (^2) primes) | ||

+ | cubes = takeWhile (<limit) (map (^3) primes) | ||

+ | fourths = takeWhile (<limit) (map (^4) primes) | ||

+ | choices = [[s,c,f] | s <- squares, c <- cubes, f <- fourths] | ||

+ | unique = map head . group . sort | ||

+ | expressible = filter (<limit) . unique . map sum $ choices | ||

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

## Revision as of 22:54, 15 August 2007

## Contents |

## 1 Problem 81

Find the minimal path sum from the top left to the bottom right by moving right and down.

Solution:

problem_81 = undefined

## 2 Problem 82

Find the minimal path sum from the left column to the right column.

Solution:

problem_82 = undefined

## 3 Problem 83

Find the minimal path sum from the top left to the bottom right by moving left, right, up, and down.

Solution:

problem_83 = undefined

## 4 Problem 84

In the game, Monopoly, find the three most popular squares when using two 4-sided dice.

Solution:

problem_84 = undefined

## 5 Problem 85

Investigating the number of rectangles in a rectangular grid.

Solution:

problem_85 = undefined

## 6 Problem 86

Exploring the shortest path from one corner of a cuboid to another.

Solution:

problem_86 = undefined

## 7 Problem 87

Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power?

Solution:

import List problem_87 = length expressible where limit = 50000000 squares = takeWhile (<limit) (map (^2) primes) cubes = takeWhile (<limit) (map (^3) primes) fourths = takeWhile (<limit) (map (^4) primes) choices = [[s,c,f] | s <- squares, c <- cubes, f <- fourths] unique = map head . group . sort expressible = filter (<limit) . unique . map sum $ choices

## 8 Problem 88

Exploring minimal product-sum numbers for sets of different sizes.

Solution:

problem_88 = undefined

## 9 Problem 89

Develop a method to express Roman numerals in minimal form.

Solution:

problem_89 = undefined

## 10 Problem 90

An unexpected way of using two cubes to make a square.

Solution:

problem_90 = undefined