From 6ff5195bc11282f333badb66a40da4309cc2a247 Mon Sep 17 00:00:00 2001
From: Daniel <dstair@hotmail.com>
Date: Sun, 22 Jun 2014 22:28:31 -0400
Subject: [PATCH] Completed Euler Problems

---
 problem03.rb | 21 +++++++++++++++++++++
 problem05.rb | 24 ++++++++++++++++++++++++
 problem08.rb | 35 +++++++++++++++++++++++++++++++++++
 3 files changed, 80 insertions(+)

diff --git a/problem03.rb b/problem03.rb
index e69de29..7eab97d 100644
--- a/problem03.rb
+++ b/problem03.rb
@@ -0,0 +1,21 @@
+# Goal: Answer the question "What is the largest prime factor of the number 600851475143?"
+# Project Euler - Problem 3
+# Daniel Stair
+
+
+require 'prime'
+
+# start at half the number given (round down if decimal). Next smallest prime factor can't exceed this amount
+testnum = 600851475143
+max_factor = Math.sqrt(testnum)
+prime_factor_array = []
+
+for i in 1..max_factor
+  if testnum.to_f % i.to_f == 0 && i.prime?
+    # add it to a list of all prime factors
+    prime_factor_array << i
+  end
+end
+
+puts "Valid prime factors of "+testnum.to_s+" are "+prime_factor_array.to_s
+puts "the largest prime factor of "+testnum.to_s+" is "+prime_factor_array.max.to_s
diff --git a/problem05.rb b/problem05.rb
index e69de29..6387d68 100644
--- a/problem05.rb
+++ b/problem05.rb
@@ -0,0 +1,24 @@
+# What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
+# Project Euler - Problem 5
+# Daniel Stair
+
+# Outer loop counts up from 1 (though it only needs to go from 2520 I think) (use i)
+i = 1
+
+while i < 240000000
+  # initialize our variables
+  j = 0
+  k = true
+  
+  # Inner loop divides outer loop's number by each number from 1 to 20 (use j)
+    while j < 21 and k == true    
+      k = i.to_f % j.to_f == 0
+      j += 1
+    
+      if j == 20 and k == true
+        puts i.to_i.to_s + " PASSES"
+      end
+    end
+  # increment by 20 since we know the answer has to be divisible by 20
+  i += 20
+end
\ No newline at end of file
diff --git a/problem08.rb b/problem08.rb
index e69de29..8996a93 100644
--- a/problem08.rb
+++ b/problem08.rb
@@ -0,0 +1,35 @@
+# Project Euler - Problem 8
+# Daniel Stair
+
+
+testnums = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450".to_s
+
+
+puts "Iterating through " + testnums.length.to_s + " numbers"
+
+# brute force method
+i = 0
+j = 0
+maxproduct = 0
+max_i = 0
+
+# loop through length of string
+while i <= 100
+    product = \
+    testnums[i].to_i*testnums[i+1].to_i*testnums[i+2].to_i*testnums[i+3].to_i* \
+    testnums[i+4].to_i*testnums[i+5].to_i*testnums[i+6].to_i*testnums[i+7].to_i*\
+    testnums[i+8].to_i*testnums[i+9].to_i*testnums[i+10].to_i*testnums[i+11].to_i*\
+    testnums[i+12].to_i
+    puts product
+
+    if product > maxproduct
+      maxproduct = product
+      max_i = i
+    end
+
+    i += 1
+end
+
+puts "the end max product is " + maxproduct.to_s
+puts "this occurred starting at the " + max_i.to_s + "th number"
+puts "sequence is: " + testnums[max_i..max_i+12]
\ No newline at end of file