# Euler problems/91 to 100

## 1 Problem 91

Find the number of right angle triangles in the quadrant.

Solution:

```reduce x y = (quot x d, quot y d)
where d = gcd x y

problem_91 n = 3*n*n + 2* sum others
where
others = do
x1 <- [1..n]
y1 <- [1..n]
let (yi,xi) = reduce x1 y1
let yc = quot (n-y1) yi
let xc = quot x1 xi
return (min xc yc)```

## 2 Problem 92

Investigating a square digits number chain with a surprising property.

Solution:

`problem_92 = undefined`

## 3 Problem 93

Using four distinct digits and the rules of arithmetic, find the longest sequence of target numbers.

Solution:

`problem_93 = undefined`

## 4 Problem 94

Investigating almost equilateral triangles with integral sides and area.

Solution:

`problem_94 = undefined`

## 5 Problem 95

Find the smallest member of the longest amicable chain with no element exceeding one million.

Solution which avoid visiting a number more than one time :

```import Data.Array.Unboxed
import qualified Data.IntSet as S
import Data.List

takeUntil _ [] = []
takeUntil pred (x:xs) = x : if pred x then takeUntil pred xs else []

chain n s =  lgo [n] \$ properDivisorsSum ! n
where lgo xs x | x > 1000000 || S.notMember x s = (xs,[])
| x `elem` xs = (xs,x : takeUntil (/= x) xs)
| otherwise = lgo (x:xs) \$ properDivisorsSum ! x

properDivisorsSum = accumArray (+) 1 (0,1000000)
\$ (0,-1):[(k,factor)|
factor<-[2..1000000 `div` 2]
, k<-[2*factor,2*factor+factor..1000000]
]

base = S.fromList [1..1000000]

problem_95 = fst \$ until (S.null . snd) f ((0,0),base)
where
f (p@(n,m), s) = (p', s')
where
setMin = head \$ S.toAscList s
(explored, chn) = chain setMin s
len = length chn
p' = if len > m then (minimum chn, len) else p
s' = foldl' (flip S.delete) s explored```

## 6 Problem 96

Devise an algorithm for solving Su Doku puzzles.

Solution:

`problem_96 = undefined`

## 7 Problem 97

Find the last ten digits of the non-Mersenne prime: 28433 × 27830457 + 1.

Solution:

`problem_97 = (28433 * 2^7830457 + 1) `mod` (10^10)`

## 8 Problem 98

Investigating words, and their anagrams, which can represent square numbers.

Solution:

`problem_98 = undefined`

## 9 Problem 99

Which base/exponent pair in the file has the greatest numerical value?

Solution:

`problem_99 = undefined`

## 10 Problem 100

Finding the number of blue discs for which there is 50% chance of taking two blue.

Solution:

`problem_100 = undefined`