From b3831fb36056c7c3f00334f096ace036b46ba905 Mon Sep 17 00:00:00 2001
From: MitchellHansen <mitchellhansen4@gmail.com>
Date: Sun, 23 Apr 2017 22:19:11 -0700
Subject: [PATCH] Few more problems

---
 problem_26.py | 35 ++++++++++++++++++++++++++++-------
 problem_27.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 problem_28.py | 29 +++++++++++++++++++++++++++++
 problem_29.py | 12 ++++++++++++
 problem_30.py | 15 +++++++++++++++
 problem_31.py | 45 +++++++++++++++++++++++++++++++++++++++++++++
 6 files changed, 172 insertions(+), 7 deletions(-)
 create mode 100644 problem_27.py
 create mode 100644 problem_28.py
 create mode 100644 problem_29.py
 create mode 100644 problem_30.py
 create mode 100644 problem_31.py

diff --git a/problem_26.py b/problem_26.py
index 0a0b675..909e0d7 100644
--- a/problem_26.py
+++ b/problem_26.py
@@ -10,16 +10,37 @@
 # 1/8	= 	0.125
 # 1/9	= 	0.(1)
 # 1/10	= 	0.1
-
+#
 # Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
 #
 # Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
 
-def longest_permutation(input):
+def longest_permutation(denominator):
+
+    mod_list = []
+    modulo = 1.0
+
+    while True:
+
+        modulo *= 10
+        if modulo in mod_list:
+            break
+
+        mod_list.append(modulo)
+        modulo %= denominator
+
+    return len(mod_list)
+
+longest_perm = 0
+longest_perm_denominator = 0
+
+for i in range(1, 1000):
+
+    perm_num = longest_permutation(i)
 
-    return input
+    if longest_perm < perm_num:
+        longest_perm = perm_num
+        longest_perm_denominator = i
 
-i = str(1.0/7.0)
-print(i)
-if "142857" in i:
-    print(True)
\ No newline at end of file
+print(longest_perm_denominator)
+print(longest_perm)
diff --git a/problem_27.py b/problem_27.py
new file mode 100644
index 0000000..71f3115
--- /dev/null
+++ b/problem_27.py
@@ -0,0 +1,43 @@
+import math
+
+# n^2 + a*n + b , where |a|<1000 and |b|<1000
+
+
+def is_prime(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
+
+largest_n = 0
+largest_n_a = 0
+largest_n_b = 0
+
+for a in range(-1000, 1000):
+    for b in range(-1000, 1000):
+
+        n = 1
+        while True:
+            if not is_prime(abs(n*n + a*n + b)):
+                break
+            else:
+                n += 1
+
+        if n > largest_n:
+            largest_n = n
+            largest_n_a = a
+            largest_n_b = b
+
+    print("{0}, {1}".format(a, b))
+
+print(largest_n)
+print(largest_n_a)
+print(largest_n_b)
\ No newline at end of file
diff --git a/problem_28.py b/problem_28.py
new file mode 100644
index 0000000..0468260
--- /dev/null
+++ b/problem_28.py
@@ -0,0 +1,29 @@
+
+# What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
+
+# top right
+tr_sum = 1
+for i in range(1, 501):
+    tr_sum += pow(i * 2 + 1, 2)
+
+# bottom right
+br_sum = 1
+br_tmp = 1
+for i in range(1, 501):
+    br_tmp += 2 + 8 * (i-1)
+    br_sum += br_tmp
+
+# bottom left
+bl_sum = 1
+for i in range(1, 501):
+    bl_sum += pow(i * 2, 2) + 1
+
+# top left
+tl_sum = 1
+tl_tmp = 1
+for i in range(1, 501):
+    tl_tmp += (i-1) * 8 + 6
+    tl_sum += tl_tmp
+
+# I guess the problem is looking to not repeat the center case to take away 3
+print(tl_sum + bl_sum + br_sum + tr_sum - 3)
\ No newline at end of file
diff --git a/problem_29.py b/problem_29.py
new file mode 100644
index 0000000..46849e1
--- /dev/null
+++ b/problem_29.py
@@ -0,0 +1,12 @@
+import itertools
+
+set_list = set()
+
+permutation_list = list(itertools.product(range(2, 101), range(2, 101)))
+
+for i in permutation_list:
+    set_list.add(pow(i[0], i[1]))
+
+print(len(set_list))
+
+
diff --git a/problem_30.py b/problem_30.py
new file mode 100644
index 0000000..ddb9e89
--- /dev/null
+++ b/problem_30.py
@@ -0,0 +1,15 @@
+
+
+total_sum = 0
+
+# just gonna take a wild guess and say there aren't any more higher than 1 million
+for i in range(2, 1000000):
+    num_str = str(i)
+    sum = 0
+    for ch in num_str:
+        sum += pow(int(ch), 5)
+    if sum == i:
+        print(i)
+        total_sum += i
+
+print("Total sum {0}".format(total_sum))
\ No newline at end of file
diff --git a/problem_31.py b/problem_31.py
new file mode 100644
index 0000000..7021e35
--- /dev/null
+++ b/problem_31.py
@@ -0,0 +1,45 @@
+
+# solving this recursively is an interesting solution
+
+import itertools
+
+set_list = set()
+permutation_list = list(itertools.combinations(list([1, 2, 5, 10, 20, 50, 100, 200]), 2))
+
+success_count = 0
+
+
+def recursive_coin_add(value, ciel):
+
+    if value == ciel:
+        global success_count
+        success_count += 1
+        return
+
+    if 1 + value <= ciel:
+        recursive_coin_add(1 + value, ciel)
+
+    if 2 + value <= ciel:
+        recursive_coin_add(2 + value, ciel)
+
+    if 5 + value <= ciel:
+        recursive_coin_add(5 + value, ciel)
+
+    if 10 + value <= ciel:
+        recursive_coin_add(10 + value, ciel)
+
+    if 20 + value <= ciel:
+        recursive_coin_add(20 + value, ciel)
+
+    if 50 + value <= ciel:
+        recursive_coin_add(50 + value, ciel)
+
+    if 100 + value <= ciel:
+        recursive_coin_add(100 + value, ciel)
+
+    if 200 + value <= ciel:
+        recursive_coin_add(200 + value, ciel)
+
+recursive_coin_add(0, 200)
+
+print(success_count)
\ No newline at end of file