From 6bee470b8ae70775a9efbf4d87f0f45a6afc8f29 Mon Sep 17 00:00:00 2001
From: Bill Ewanick <bill@ewanick.com>
Date: Thu, 28 Sep 2023 16:13:48 -0400
Subject: [PATCH] Add questions 1-3

---
 .vscode/settings.json         |  2 ++
 src/projectEuler/question1.hs | 28 ++++++++++++++++++++++++++++
 src/projectEuler/question2.hs | 16 ++++++++++++++++
 src/projectEuler/question3.hs | 34 ++++++++++++++++++++++++++++++++++
 4 files changed, 80 insertions(+)
 create mode 100644 src/projectEuler/question1.hs
 create mode 100644 src/projectEuler/question2.hs
 create mode 100644 src/projectEuler/question3.hs

diff --git a/.vscode/settings.json b/.vscode/settings.json
index 9700597..74f9a48 100644
--- a/.vscode/settings.json
+++ b/.vscode/settings.json
@@ -4,6 +4,8 @@
     "concat",
     "coprime",
     "elems",
+    "Factorisation",
+    "factorise",
     "foldl"
   ]
 }
\ No newline at end of file
diff --git a/src/projectEuler/question1.hs b/src/projectEuler/question1.hs
new file mode 100644
index 0000000..3b25706
--- /dev/null
+++ b/src/projectEuler/question1.hs
@@ -0,0 +1,28 @@
+{-
+https://projecteuler.net/problem=1
+If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9.
+The sum of these multiples is 23.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
+-}
+module Main where
+
+main :: IO ()
+main = print ans
+
+ans :: Integer
+ans = sum $ allNumbersUnder 1000
+
+isMultipleOf :: Integral a => a -> a -> Bool
+isMultipleOf n x = x `rem` n == 0
+
+all3sUnder :: Integral a => a -> [a]
+all3sUnder n = filter (isMultipleOf 3) [1..n-1]
+all5sUnder :: Integral a => a -> [a]
+all5sUnder n = filter (isMultipleOf 5) [1..n-1]
+
+allXsUnderN :: Integral a => a -> a -> [a]
+allXsUnderN x n = filter (isMultipleOf x) [1..n-1]
+
+allNumbersUnder :: Integral a => a -> [a]
+allNumbersUnder l = allXsUnderN 3 l <> allXsUnderN 5 l
diff --git a/src/projectEuler/question2.hs b/src/projectEuler/question2.hs
new file mode 100644
index 0000000..92016bf
--- /dev/null
+++ b/src/projectEuler/question2.hs
@@ -0,0 +1,16 @@
+{-
+https://projecteuler.net/problem=2
+Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...
+
+By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
+-}
+module Main where
+
+main :: IO ()
+main = print ans
+
+ans = sum $ filter even $ takeWhile(< 4_000_000) fibs
+
+fibs = 1 : 2 : zipWith (+) fibs (tail fibs)
diff --git a/src/projectEuler/question3.hs b/src/projectEuler/question3.hs
new file mode 100644
index 0000000..a27997c
--- /dev/null
+++ b/src/projectEuler/question3.hs
@@ -0,0 +1,34 @@
+{-
+https://projecteuler.net/problem=3
+
+The prime factors of 13195 are 5, 7, 13, and 29.
+
+What is the largest prime factor of the number 600851475143?
+-}
+module Main where
+
+import           Math.NumberTheory.Primes (Prime (unPrime),
+                                           UniqueFactorisation (factorise),
+                                           primes)
+
+main :: IO ()
+main = print ans
+
+ans :: Int
+ans = last $ filter (isFactor bigNum) primes'
+
+primes' :: [Int]
+primes' = takeWhile (< sqrt') $ map unPrime primes
+  where
+    sqrt' = floor $ sqrt (toEnum bigNum)
+
+bigNum :: Int
+bigNum = 600851475143
+
+isFactor :: Int -> Int -> Bool
+isFactor x n = x `rem` n == 0
+
+ans' :: [Int]
+ans' = map (unPrime . fst) $ factorise (fromEnum bigNum)
+-- [(Prime 71,1),(Prime 839,1),(Prime 1471,1),(Prime 6857,1)]
+-- [71,839,1471,6857]