# Euler problems/81 to 90

## 1 Problem 81

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

Solution:

```import Data.List (unfoldr)

columns s = unfoldr f s
where
f [] = Nothing
f xs = Just \$ (\(a,b) -> (read a, drop 1 b)) \$ break (==',') xs

firstLine ls = scanl1 (+) ls

nextLine pl [] = pl
nextLine pl (n:nl) = nextLine p' nl
where
p' = nextCell (head pl) pl n
nextCell _ [] [] = []
nextCell pc (p:pl) (n:nl) = pc' : nextCell pc' pl nl
where pc' = n + min p pc

minSum (p:nl) = last \$ nextLine p' nl
where
p' = firstLine p

problem_81 c = minSum \$ map columns \$ lines c```

## 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`