Merge branch 'manwar:master' into master

2 files changed, 110 insertions, 0 deletions

diff --git a/challenge-169/sgreen/python/ch-1.py b/challenge-169/sgreen/python/ch-1.py
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+++ b/challenge-169/sgreen/python/ch-1.py
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+#!/usr/bin/env python3
+
+import math
+
+
+def is_prime(number):
+    '''Return true or false if the number is a prime'''
+    if number < 2:
+        return False
+
+    for i in range(2, int(math.sqrt(number)) + 1):
+        if number % i == 0:
+            return False
+
+    # It's a prime
+    return True
+
+
+def get_bril_nums(l):
+    '''Get all primes of length l'''
+
+    primes = []
+    for i in range(10**(l-1), 10**l):
+        if is_prime(i):
+            primes.append(i)
+
+    # Calculate all brilliant numbers
+    bril_nums = []
+    for i, v1 in enumerate(primes):
+        for v2 in primes[i:]:
+            bril_nums.append(v1*v2)
+
+    # Return the sorted list
+    bril_nums.sort()
+    return bril_nums
+
+
+def main():
+    '''Find the first twenty brilliant numbers'''
+    l = 1
+    bril_nums = []
+
+    # Keep increasing the length of primes until we have at least twenty
+    #  solutions
+    while len(bril_nums) < 20:
+        bril_nums.extend(get_bril_nums(l))
+        l += 1
+
+    # Print the first 20 numbers
+    print(*bril_nums[0:20], sep=', ')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/challenge-169/sgreen/python/ch-2.py b/challenge-169/sgreen/python/ch-2.py
new file mode 100755
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+++ b/challenge-169/sgreen/python/ch-2.py
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+#!/usr/bin/env python3
+
+def is_achilles_number(num):
+    '''Determine if this number is an achilles numbers'''
+
+    # Get the prime factors of the number
+    factors = {}
+
+    i = 2
+    while num > 1:
+        if num % i == 0:
+            num /= i
+            if i in factors:
+                factors[i] += 1
+            else:
+                factors[i] = 1
+        else:
+            i += 1
+
+    # If there is only one prime factor, it is not an achilles number
+    if len(factors) == 1:
+        return False
+
+    # Get a list of unique powers
+    powers = set(factors.values())
+
+    # It's also not an achilles number if any of the powers were 1, or the
+    #  powers are all the same (a perfect sqaure)
+    if 1 in powers or len(powers) == 1:
+        return False
+
+    # Finally, the greatest common divisor of these numbers has to be one
+    for i in range(2, min(powers)+1):
+        if all(x % i == 0 for x in powers):
+            return False
+
+    return True
+
+
+def main():
+    '''Find the first 20 achilles numbers'''
+    solutions = []
+    num = 2
+
+    # Get the first 20 achilles numbers
+    while len(solutions) < 20:
+        if is_achilles_number(num):
+            solutions.append(num)
+        num += 1
+
+    # Print the list
+    print(*solutions, sep=', ')
+
+
+if __name__ == '__main__':
+    main()