Solve problem 243.

python/e243.py

@@ -0,0 +1,40 @@
+from math import gcd
+from fractions import Fraction
+
+
+def product(xs):
+    r = 1
+    for x in xs:
+        r *= x
+    return r
+
+
+def ratio(d):
+    r = 0
+    for i in range(1, d):
+        if gcd(i, d) == 1:
+            r += 1
+    return Fraction(r, (d - 1))
+
+
+def euler_243():
+    target = Fraction(15499, 94744)  # 0.1635881955585578
+
+    # The more prime factors, the lower the initial fraction gets. We figure
+    # out empirically that using primes up to 23 yields results close to the
+    # target fraction. We then iterate over the multiples to find the
+    # solution.
+    factors = [2, 3, 5, 7, 11, 13, 17, 19, 23]
+
+    for mul in range(1, 10):
+        d = mul * product(factors)
+        r = ratio(d)
+        if r < target:
+            return d
+    return None
+
+
+if __name__ == "__main__":
+    solution = euler_243()
+    print("e243.py: " + str(solution))
+    assert(solution == 892371480)