From b6b10cdd1248aaa87e37d09221ba4bbaac1e6f61 Mon Sep 17 00:00:00 2001
From: Daniele Fucini <dfucini@gmail.com>
Date: Mon, 1 Apr 2024 15:19:09 +0200
Subject: [PATCH] Add Haskell solutions for Problems 4, 5, 6, 7

---
 Haskell/p004.hs | 15 +++++++++++++++
 Haskell/p005.hs | 13 +++++++++++++
 Haskell/p006.hs | 19 +++++++++++++++++++
 Haskell/p007.hs | 13 +++++++++++++
 4 files changed, 60 insertions(+)
 create mode 100644 Haskell/p004.hs
 create mode 100644 Haskell/p005.hs
 create mode 100644 Haskell/p006.hs
 create mode 100644 Haskell/p007.hs

diff --git a/Haskell/p004.hs b/Haskell/p004.hs
new file mode 100644
index 0000000..3040842
--- /dev/null
+++ b/Haskell/p004.hs
@@ -0,0 +1,15 @@
+-- A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
+--
+-- Find the largest palindrome made from the product of two 3-digit numbers.
+
+isPalindrome :: Integer -> Bool
+isPalindrome n = show n == (reverse $ show n)
+
+maxPalindrome :: Integer
+maxPalindrome =
+    maximum $ filter isPalindrome [ x * y | x <- [100..999], y <- [100..999] ]
+
+main = do
+    let result = maxPalindrome
+    putStrLn $ "Project Euler, Problem 4\n"
+        ++ "Answer: " ++ (show result)
diff --git a/Haskell/p005.hs b/Haskell/p005.hs
new file mode 100644
index 0000000..d74decc
--- /dev/null
+++ b/Haskell/p005.hs
@@ -0,0 +1,13 @@
+-- 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+--
+-- What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
+
+lcmm :: (Integral n) => [n] -> n
+lcmm values
+    | length values == 2    = lcm (head values) (last values)
+    | otherwise             = lcm (head values) (lcmm (tail values))
+
+main = do
+    let result = lcmm [1..20]
+    putStrLn $ "Project Euler, Problem 5\n"
+        ++ "Answer: " ++ (show result)
diff --git a/Haskell/p006.hs b/Haskell/p006.hs
new file mode 100644
index 0000000..d6cb483
--- /dev/null
+++ b/Haskell/p006.hs
@@ -0,0 +1,19 @@
+-- The sum of the squares of the first ten natural numbers is,
+--
+-- 1^2 + 2^2 + ... + 10^2 = 385
+--
+-- The square of the sum of the first ten natural numbers is,
+--
+-- (1 + 2 + ... + 10)^2 = 55^2 = 3025
+--
+-- Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.
+--
+--Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
+
+sumSquareDiff :: Integer -> Integer
+sumSquareDiff n = (sum [1..n]^2) - (sum $ map (^2) [1..n])
+
+main = do
+    let result = sumSquareDiff 100
+    putStrLn $ "Project Euler, Problem 6\n"
+        ++ "Answer: " ++ (show result)
diff --git a/Haskell/p007.hs b/Haskell/p007.hs
new file mode 100644
index 0000000..a1ea5ed
--- /dev/null
+++ b/Haskell/p007.hs
@@ -0,0 +1,13 @@
+-- By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
+--
+-- What is the 10 001st prime number?
+--
+import ProjectEuler (isPrime)
+
+nthPrime :: (Integral a) => Int -> a
+nthPrime n = last $ take n [ x | x <- [1..], isPrime x ]
+
+main = do
+    let result = nthPrime 10001
+    putStrLn $ "Project Euler, Problem 7\n"
+        ++ "Answer: " ++ (show result)