problem 3 4 5 6 6 in julia

5 files changed, 134 insertions, 0 deletions

diff --git a/julia/003-largest_prime_factor.jl b/julia/003-largest_prime_factor.jl
new file mode 100644
index 0000000..01e71cf
--- /dev/null
+++ b/julia/003-largest_prime_factor.jl
@@ -0,0 +1,25 @@
+###
+# Largest prime factor
+# Problem 3
+#
+# The prime factors of 13195 are 5, 7, 13 and 29.
+# What is the largest prime factor of the number 600851475143 ?
+###
+
+const NUMBER = 600851475143
+
+function factors(n)
+    factors = []
+    while n > 1
+        for d in 2:n
+            if n % d == 0
+                n = Int64(n / d)
+                push!(factors, d)
+                break
+            end
+        end
+    end
+    factors
+end
+
+println(maximum(factors(NUMBER)))
diff --git a/julia/004-largest_palindrome_product.jl b/julia/004-largest_palindrome_product.jl
new file mode 100644
index 0000000..32be760
--- /dev/null
+++ b/julia/004-largest_palindrome_product.jl
@@ -0,0 +1,26 @@
+###
+# Largest palindrome product
+# Problem 4
+#
+# 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.
+###
+
+function is_palindrom(n)
+    s = string(n)
+    s == reverse(s)
+end
+
+
+top = -1
+
+for x in 100:999
+    for y in 100:999
+        if is_palindrom(x * y)
+            global top = max(top, x * y)
+        end
+    end
+end
+
+println(top)
diff --git a/julia/005-smallest_multiple.jl b/julia/005-smallest_multiple.jl
new file mode 100644
index 0000000..e938baf
--- /dev/null
+++ b/julia/005-smallest_multiple.jl
@@ -0,0 +1,26 @@
+###
+# Smallest multiple
+# Problem 5
+#
+# 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?
+###
+
+using Base.Iterators
+
+for n in Iterators.countfrom(2, 2)
+    # any(d -> n % d != 0, reverse(2:20)) && continue
+    found = true
+    for d in reverse(2:20)
+        if n % d != 0
+            found = false
+            break
+        end
+    end
+    if found
+        println(n)
+        break
+    end
+end
diff --git a/julia/006-sum_square_difference.jl b/julia/006-sum_square_difference.jl
new file mode 100644
index 0000000..39e5df8
--- /dev/null
+++ b/julia/006-sum_square_difference.jl
@@ -0,0 +1,20 @@
+###
+# Sum square difference
+# Problem 6
+#
+# 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.
+###
+
+const count = 100
+
+sum_of_squares = sum(x ^ 2 for x in 1:count)
+square_of_sum  = sum(1:count) ^ 2
+
+println(square_of_sum - sum_of_squares)
diff --git a/julia/007-10001st_prime.jl b/julia/007-10001st_prime.jl
new file mode 100644
index 0000000..6928484
--- /dev/null
+++ b/julia/007-10001st_prime.jl
@@ -0,0 +1,37 @@
+###
+# 10001st prime
+# Problem 7
+#
+# 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?
+###
+
+using Printf
+using Base.Iterators
+
+function is_prime(n)
+    if n == 2 || n == 3 || n == 5
+        return true
+    end
+    if n % 2 == 0 || n % 3 == 0 || n % 5 == 0
+        return false
+    end
+    for d in 6:6:Int64(ceil(sqrt(n)) + 1)
+        if n % (d - 1) == 0 || n % (d + 1) == 0
+            return false
+        end
+    end
+    true
+end
+
+counter = 0
+for n in Iterators.countfrom(2)
+    if is_prime(n)
+        global counter += 1
+        @printf "%5d: %d\n" counter n
+    end
+    if counter == 10_001
+        break
+    end
+end