Solves problem 41

problem41.py

@@ -0,0 +1,45 @@
+"""
+We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once.
+For example, 2143 is a 4-digit pandigital and is also prime.
+
+What is the largest n-digit pandigital prime that exists?
+"""
+
+from utilities import divisors
+from itertools import permutations
+
+
+def largest_pandigital_prime(n):
+    digits = sorted(xrange(1, n + 1), reverse=True)
+    for comb in permutations(digits):
+
+        if comb[-1] in (0, 2, 4, 5, 6, 8):
+            # Even numbers and multiples of 5 are obviously not prime
+            continue
+
+        num = int(''.join(str(d) for d in comb))
+        if any(divisors(num, only_primes=True, only_proper=True)):
+            continue
+        else:
+            return num
+    else:
+        return None
+
+
+if __name__ == '__main__':
+
+    # The solution can't have 5, 6, 8 or 9 digits because:
+    # sum(1..9) = 45
+    # sum(1..8) = 36
+    # sum(1..6) = 21
+    # sum(1..5) = 15
+    # So every pandigital number with that number of digits is divisible by 3
+    # The problem text tells you that 2143 is prime, therefore the solution must be at least 4 digits long
+    # and this rules out 3 too.
+    candidate_n = [7, 4]
+
+    for n in candidate_n:
+        p = largest_pandigital_prime(n)
+        if p:
+            print p
+            break