From 7beaeae01402bd038bce9263e7f0a11665be4a4d Mon Sep 17 00:00:00 2001
From: Daniel Ingram <ingramds@appstate.edu>
Date: Wed, 14 Mar 2018 14:35:16 -0400
Subject: [PATCH 1/5] Brute force solution to Problem 10

---
 Project Euler/Problem 10/sol1.py | 33 ++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 Project Euler/Problem 10/sol1.py

diff --git a/Project Euler/Problem 10/sol1.py b/Project Euler/Problem 10/sol1.py
new file mode 100644
index 000000000..ca9593afa
--- /dev/null
+++ b/Project Euler/Problem 10/sol1.py	
@@ -0,0 +1,33 @@
+from __future__ import print_function
+from math import sqrt
+
+def is_prime(n):
+	for i in xrange(2, int(sqrt(n))+1):
+		if n%i == 0:
+			return False
+
+	return True
+
+def sum_of_primes(n):
+	if n > 2:
+		sumOfPrimes = 2
+	else:
+		return 0
+
+	for i in xrange(3, n, 2):
+		if is_prime(i):
+			sumOfPrimes += i
+
+	return sumOfPrimes
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		print(sum_of_primes(2000000))
+	else:
+		try:
+			n = int(sys.argv[1])
+			print(sum_of_primes(n))
+		except ValueError:
+			print('Invalid entry - please enter a number.')
\ No newline at end of file

From 301c90737674b9724be03fe7d25e5314cf406a04 Mon Sep 17 00:00:00 2001
From: Daniel Ingram <ingramds@appstate.edu>
Date: Wed, 14 Mar 2018 14:55:07 -0400
Subject: [PATCH 2/5] Dynamic programming solution to Problem 25

---
 Project Euler/Problem 25/sol1.py | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)
 create mode 100644 Project Euler/Problem 25/sol1.py

diff --git a/Project Euler/Problem 25/sol1.py b/Project Euler/Problem 25/sol1.py
new file mode 100644
index 000000000..67185774d
--- /dev/null
+++ b/Project Euler/Problem 25/sol1.py	
@@ -0,0 +1,26 @@
+from __future__ import print_function
+
+def fibonacci(n):
+	if n == 1 or type(n) is not int:
+		return 0
+	elif n == 2:
+		return 1
+	else:
+		sequence = [0, 1]
+		for i in xrange(2, n+1):
+			sequence.append(sequence[i-1] + sequence[i-2])
+
+		return sequence[n]
+
+def fibonacci_digits_index(n):
+	digits = 0
+	index = 2
+
+	while digits < n:
+		index += 1
+		digits = len(str(fibonacci(index)))
+
+	return index
+
+if __name__ == '__main__':
+	print(fibonacci_digits_index(1000))
\ No newline at end of file

From ac14455ac0448e0fb34221a316f4d9c48ab37107 Mon Sep 17 00:00:00 2001
From: Daniel Ingram <ingramds@appstate.edu>
Date: Wed, 14 Mar 2018 15:39:52 -0400
Subject: [PATCH 3/5] Combinatoric solution using Pascal's Triangle to Problem
 15

---
 Project Euler/Problem 15/sol1.py | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)
 create mode 100644 Project Euler/Problem 15/sol1.py

diff --git a/Project Euler/Problem 15/sol1.py b/Project Euler/Problem 15/sol1.py
new file mode 100644
index 000000000..9b61b37d2
--- /dev/null
+++ b/Project Euler/Problem 15/sol1.py	
@@ -0,0 +1,20 @@
+from __future__ import print_function
+from math import factorial, ceil
+
+def lattice_paths(n):
+	n = 2*n #middle entry of odd rows starting at row 3 is the solution for n = 1, 2, 3,...
+	k = n/2
+
+	return factorial(n)/(factorial(k)*factorial(n-k))
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		print(lattice_paths(20))
+	else:
+		try:
+			n = int(sys.argv[1])
+			print(lattice_paths(n))
+		except ValueError:
+			print('Invalid entry - please enter a number.')

From 7704151504d38433bb7490298576dfbb604280b6 Mon Sep 17 00:00:00 2001
From: Daniel Ingram <ingramds@appstate.edu>
Date: Wed, 14 Mar 2018 16:03:44 -0400
Subject: [PATCH 4/5] Solution to Problem 28

---
 Project Euler/Problem 28/sol1.py | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)
 create mode 100644 Project Euler/Problem 28/sol1.py

diff --git a/Project Euler/Problem 28/sol1.py b/Project Euler/Problem 28/sol1.py
new file mode 100644
index 000000000..7944caa21
--- /dev/null
+++ b/Project Euler/Problem 28/sol1.py	
@@ -0,0 +1,23 @@
+from __future__ import print_function
+
+def diagonal_sum(n):
+	total = 1
+
+	for i in xrange(n/2):
+		odd = 2*(i+1)+1
+		even = 2*(i+1)
+		total = total + 4*odd**2 - 6*even
+
+	return total
+
+if __name__ == '__main__':
+	import sys
+
+	if len(sys.argv) == 1:
+		print(diagonal_sum(1001))
+	else:
+		try:
+			n = int(sys.argv[1])
+			diagonal_sum(n)
+		except ValueError:
+			print('Invalid entry - please enter a number')
\ No newline at end of file

From 81dc221ee28f7e34e0293d08df11214cf9d06d5e Mon Sep 17 00:00:00 2001
From: Daniel Ingram <ingramds@appstate.edu>
Date: Wed, 14 Mar 2018 17:18:59 -0400
Subject: [PATCH 5/5] Solution to Problem 28

---
 Project Euler/Problem 28/sol1.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/Project Euler/Problem 28/sol1.py b/Project Euler/Problem 28/sol1.py
index 7944caa21..d44d01789 100644
--- a/Project Euler/Problem 28/sol1.py	
+++ b/Project Euler/Problem 28/sol1.py	
@@ -1,11 +1,12 @@
 from __future__ import print_function
+from math import ceil
 
 def diagonal_sum(n):
 	total = 1
 
-	for i in xrange(n/2):
-		odd = 2*(i+1)+1
-		even = 2*(i+1)
+	for i in xrange(1, int(ceil(n/2.0))):
+		odd = 2*i+1
+		even = 2*i
 		total = total + 4*odd**2 - 6*even
 
 	return total