Solve problem 173.

python/e173.py

@@ -0,0 +1,57 @@
+
+
+def tiles(size):
+    """ Returns the number of tiles for a square of the given size. """
+    return size * 4 - 4
+
+
+def tiles_for_outer(size):
+    """ Returns the number of tiles for all possible laminae given the size of
+    the outermost ring. """
+
+    n_outer = tiles(size)
+    r = [n_outer]
+    for ni in range(size - 2, 2, -2):
+        n_outer += tiles(ni)
+        r.append(n_outer)
+    return r
+
+
+def count_tiles(size, n_max):
+
+    """ Count how many possible laminae with a size smaller the `n_max` are
+    possible for the given outermost ring `size`. """
+
+    n_outer = tiles(size)
+    if n_outer > n_max:
+        return 0
+
+    count = 1
+    for ni in range(size - 2, 2, -2):
+        n_outer += tiles(ni)
+        if n_outer > n_max:
+            break
+        count += 1
+    return count
+
+
+def euler_173():
+    assert tiles(3) == 8
+    assert tiles(4) == 12
+    assert tiles(6) == 20
+    assert tiles(9) == 32
+
+    count = 0
+    n_max = 10**6
+    edge_length = 3
+    for edge_length in range(3, n_max):
+        if tiles(edge_length) > n_max:
+            break
+        count += count_tiles(edge_length, n_max)
+    return count
+
+
+if __name__ == "__main__":
+    solution = euler_173()
+    print("e173.py: " + str(solution))
+    assert solution == 1572729