Add more solutions

problem-55.py

@@ -0,0 +1,23 @@
+
+def get_palindrome(num):
+    return int(str(num)[::-1])
+
+
+def is_palindrome(num):
+    return get_palindrome(num) == num
+
+
+if __name__ == '__main__':
+
+    results = []
+    for i in range(10, 10000):
+        num = i + get_palindrome(i)
+        counter = 0
+        while counter < 50 and not is_palindrome(num):
+            num += get_palindrome(num)
+            counter += 1
+        if not is_palindrome(num):
+            results.append(i)
+    print(len(results))
+
+

problem-56.py

@@ -0,0 +1,12 @@
+
+MAX_NUM = 100
+
+if __name__ == '__main__':
+    maximum = 0
+    for a in range(MAX_NUM):
+        for b in range(MAX_NUM):
+            num = a ** b
+            total = sum(int(x) for x in list(str(num)))
+            if total > maximum:
+                maximum = total
+    print(maximum)

problem-57.py

@@ -0,0 +1,12 @@
+
+if __name__ == '__main__':
+    results = []
+    numerator = 3
+    denominator = 2
+    for _ in range(1000):
+        if len(str(numerator)) > len(str(denominator)):
+            results.append(str(numerator) + '/' + str(denominator))
+        denominator += numerator
+        numerator   += 2 * (denominator - numerator)
+    print(results)
+    print(len(results))

problem-65.py

@@ -0,0 +1,20 @@
+
+
+if __name__ == '__main__':
+    sequence = [2]
+
+    i = 1
+    while len(sequence) < 100:
+        sequence.extend([1, i * 2, 1])
+        i+=1
+
+    numerator = 1
+    denominator = sequence.pop()
+
+    while len(sequence) > 0:
+        frac = (sequence.pop() * denominator + numerator, denominator)
+        denominator = frac[0]
+        numerator = frac[1]
+
+    print(frac)
+    print(sum(int(i) for i in list(str(frac[0]))))

problem-69.c

@@ -0,0 +1,60 @@
+#include <stdio.h>
+
+unsigned int gcd(unsigned int u, unsigned int v)
+{
+	int shift;
+	if (u == 0) return v;
+	if (v == 0) return u;
+	shift = __builtin_ctz(u | v);
+	u >>= __builtin_ctz(u);
+	do {
+		v >>= __builtin_ctz(v);
+		if (u > v) {
+			unsigned int t = v;
+			v = u;
+			u = t;
+		}
+		v = v - u;
+	} while (v != 0);
+	return u << shift;
+}
+
+
+unsigned int is_coprime(unsigned int u, unsigned int v)
+{
+	if (gcd(u, v) == 1)
+		return 1;
+	return 0;
+}
+
+
+int main(int argc, char** argv) {
+	unsigned int i, j;
+	unsigned int coprimes;
+	unsigned int MAX_NUM = 1000000;
+	int greatest = 0;
+	double ratio = 0;
+
+	for (i=1; i<MAX_NUM; i++) {
+		if (i % 10000 == 0)
+			printf("%i\n", i);
+
+		coprimes = 1;
+		for (j = 2; j<i; j++) {
+			if (is_coprime(i, j))
+				coprimes += 1;
+		}
+
+		if (((double)i / coprimes) > greatest) {
+			greatest = i;
+			ratio = (double)i / coprimes;
+		}
+	}
+
+	printf("number: %i\n", greatest);
+	printf("ratio : %f\n", ratio);
+	return 1;
+}
+
+
+

problem-69.py

@@ -0,0 +1,20 @@
+
+from math import gcd
+
+MAX_NUM = 1000000
+
+def is_coprime(a, b):
+    return gcd(a, b) == 1
+
+
+if __name__ == '__main__':
+    greatest_ratio = (0, 0)
+    for n in range(2, MAX_NUM+1):
+        if n % 10000 == 0:
+            print(n)
+        relative_primes = len([x for x in range(2, n) if is_coprime(x, n)]) + 1
+        if n/relative_primes > greatest_ratio[1]:
+            greatest_ratio = (n, n/relative_primes)
+    print(greatest_ratio)
+
+