From 73239e1c23c763adf560eea9e154e20f14f8ae0a Mon Sep 17 00:00:00 2001
From: MitchellHansen <mitchellhansen0@gmail.com>
Date: Fri, 5 Feb 2016 21:54:01 -0800
Subject: [PATCH] Couple more problems

---
 .idea/vcs.xml |  6 +++++
 problem_10.py | 29 ++++++++++++++++++++++
 problem_11.py | 68 +++++++++++++++++++++++++++++++++++++++++++++++++++
 problem_5.py  | 25 +++++++++++++++++++
 problem_6.py  | 17 +++++++++++++
 problem_7.py  | 23 +++++++++++++++++
 problem_8.py  | 42 +++++++++++++++++++++++++++++++
 problem_9.py  | 19 ++++++++++++++
 8 files changed, 229 insertions(+)
 create mode 100644 .idea/vcs.xml
 create mode 100644 problem_10.py
 create mode 100644 problem_11.py
 create mode 100644 problem_5.py
 create mode 100644 problem_6.py
 create mode 100644 problem_7.py
 create mode 100644 problem_8.py
 create mode 100644 problem_9.py

diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..94a25f7
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>
\ No newline at end of file
diff --git a/problem_10.py b/problem_10.py
new file mode 100644
index 0000000..be7c9de
--- /dev/null
+++ b/problem_10.py
@@ -0,0 +1,29 @@
+import math
+
+#find the sum of all primes under 2 million
+#once again, it works, but it's sloooowwwww
+
+def isPrime(number):
+    if number == 1:
+        return False
+    prime = True
+    i = 2
+    while i < math.sqrt(number) + 1:
+        if number % i == 0:
+            prime = False # found a factor, not prime
+            break
+        else:
+            i += 1
+
+    return prime
+
+number = 3
+sum = 2
+
+while (number < 2000000):
+    if isPrime(number):
+        sum += number
+    number += 2
+
+print(number)
+print(sum)
\ No newline at end of file
diff --git a/problem_11.py b/problem_11.py
new file mode 100644
index 0000000..d6a525b
--- /dev/null
+++ b/problem_11.py
@@ -0,0 +1,68 @@
+#in a grid of numbers find the 4 numbers, in any orientation, that has the highest product
+
+grid = [  8, 2, 22, 97, 38, 15, 00, 40, 00, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8,
+          49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 00,
+          81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65,
+          52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91,
+          22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80,
+          24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50,
+          32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70,
+          67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21,
+          24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72,
+          21, 36, 23, 9, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95,
+          78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92,
+          16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57,
+          86, 56, 00, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58,
+          19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40,
+          4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66,
+          88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69,
+          4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36,
+          20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16,
+          20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54,
+          1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]
+
+def getItem(x, y):
+    return grid[x + int(y * 20)]
+
+highest = 0
+
+def testHighestVertical():
+    for x in range(0, 20):
+        for y in range(0, 17):
+            product = getItem(x, y) * getItem(x, y + 1) * getItem(x, y + 2) * getItem(x, y + 3)
+            global highest
+            if highest < product:
+                highest = product
+
+def testHighestHorizontal():
+    for x in range(0, 17):
+        for y in range(0, 20):
+            product = getItem(x, y) * getItem(x + 1, y) * getItem(x + 2, y) * getItem(x + 3, y)
+            global highest
+            if highest < product:
+                highest = product
+
+def testHighestDiagonalVariantOne():
+    for x in range(0, 17):
+        for y in range(0, 17):
+            product = getItem(x, y) * getItem(x + 1, y + 1) * getItem(x + 2, y + 2) * getItem(x + 3, y + 3)
+            global highest
+            if highest < product:
+                highest = product
+
+def testHighestDiagonalViariantTwo():
+    for x in range(0, 17):
+        for y in range(3, 20):
+            product = getItem(x, y) * getItem(x + 1, y - 1) * getItem(x + 2, y - 2) * getItem(x + 3, y - 3)
+            global highest
+            if highest < product:
+                highest = product
+
+
+
+testHighestDiagonalVariantOne()
+testHighestDiagonalViariantTwo()
+testHighestHorizontal()
+testHighestVertical()
+
+print(highest)
\ No newline at end of file
diff --git a/problem_5.py b/problem_5.py
new file mode 100644
index 0000000..db65527
--- /dev/null
+++ b/problem_5.py
@@ -0,0 +1,25 @@
+# Smallest positive number that is evenly divisible by all of the numbers from 1 to 20
+# Oh boy is this slow. But it works!
+
+counter = 20
+running = True
+
+def check_divisor(number):
+    q = True
+    for i in range(1, 21):
+        if number % i != 0:
+            q = False
+
+    return q
+
+while running:
+
+    if not check_divisor(counter):
+        counter += 20
+    else:
+        running = False
+
+print(counter)
+
+
+
diff --git a/problem_6.py b/problem_6.py
new file mode 100644
index 0000000..a0f2db8
--- /dev/null
+++ b/problem_6.py
@@ -0,0 +1,17 @@
+#Difference between the sum of squares and the square of the sum of the first 100 numbers
+
+#find the sum of the squares
+sum_of_squares = 0;
+for i in range (1, 101):
+    sum_of_squares += i * i
+
+#find the square of the sum
+square_of_sums = 0
+for i in range(1, 101):
+    square_of_sums += i;
+
+square_of_sums *= square_of_sums
+
+#find the difference
+square_of_sums -= sum_of_squares
+print(square_of_sums)
\ No newline at end of file
diff --git a/problem_7.py b/problem_7.py
new file mode 100644
index 0000000..45d3759
--- /dev/null
+++ b/problem_7.py
@@ -0,0 +1,23 @@
+import math
+# find the 10001st prime number
+
+def isPrime(number):
+    prime = True
+    i = 2
+    while i < math.sqrt(number) + 1:
+        if number % i == 0:
+            prime = False # found a factor, not prime
+            break
+        else:
+            i += 1
+
+    return prime
+
+i = 1;
+primeCount = 1
+while (primeCount != 10001):
+    if isPrime(i):
+        primeCount += 1
+    i += 1
+
+print(i)
\ No newline at end of file
diff --git a/problem_8.py b/problem_8.py
new file mode 100644
index 0000000..5e67fc2
--- /dev/null
+++ b/problem_8.py
@@ -0,0 +1,42 @@
+import collections
+
+# find the 13 consecutive digits with the largest product
+
+number = "73167176531330624919225119674426574742355349194934"+\
+         "96983520312774506326239578318016984801869478851843"+\
+         "85861560789112949495459501737958331952853208805511"+\
+         "12540698747158523863050715693290963295227443043557"+\
+         "66896648950445244523161731856403098711121722383113"+\
+         "62229893423380308135336276614282806444486645238749"+\
+         "30358907296290491560440772390713810515859307960866"+\
+         "70172427121883998797908792274921901699720888093776"+\
+         "65727333001053367881220235421809751254540594752243"+\
+         "52584907711670556013604839586446706324415722155397"+\
+         "53697817977846174064955149290862569321978468622482"+\
+         "83972241375657056057490261407972968652414535100474"+\
+         "82166370484403199890008895243450658541227588666881"+\
+         "16427171479924442928230863465674813919123162824586"+\
+         "17866458359124566529476545682848912883142607690042"+\
+         "24219022671055626321111109370544217506941658960408"+\
+         "07198403850962455444362981230987879927244284909188"+\
+         "84580156166097919133875499200524063689912560717606"+\
+         "05886116467109405077541002256983155200055935729725"+\
+         "71636269561882670428252483600823257530420752963450"
+
+queue = collections.deque()
+
+for i in range(0, 13):
+    queue.append(number[i])
+
+max_product = 0;
+for i in range(13, 1000):
+    product = 1
+    for q in queue:
+        product *= int(q)
+    if max_product < product:
+        max_product = product
+
+    queue.popleft()
+    queue.append(number[i])
+
+print(max_product)
\ No newline at end of file
diff --git a/problem_9.py b/problem_9.py
new file mode 100644
index 0000000..5268458
--- /dev/null
+++ b/problem_9.py
@@ -0,0 +1,19 @@
+#find the pythagorean triplet that a^2 + b^2 + c^2 = 1000
+
+#just gonna do a nested for loop for this and brute force it
+#it works, it's just slow as hell
+
+def is_triplet(a, b, c):
+    if (a < b and b < c):
+        return True
+    else:
+        return False
+
+for a in range(0, 999):
+    for b in range(0, 999):
+        for c in range(0, 999):
+            if is_triplet(a, b, c):
+                if a*a + b*b == c*c:
+                    if (a+b+c == 1000):
+                        print(a*b*c)
+                        break
\ No newline at end of file