From 8c80fdb3c1d7b9aa89752e4ae03b33f39e21a4cb Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Wed, 21 Apr 2021 12:14:57 -0400
Subject: [PATCH] Solve problem 86

---
 python/e086.py | 30 ++++++++++++++++++++++++++++--
 1 file changed, 28 insertions(+), 2 deletions(-)

diff --git a/python/e086.py b/python/e086.py
index 6bbf48b..5547d5c 100644
--- a/python/e086.py
+++ b/python/e086.py
@@ -1,9 +1,35 @@
 
+def shortest_path_squared(l, b, h):
+    s1 = l ** 2 + (h + b) ** 2
+    s2 = h ** 2 + (b + l) ** 2
+    s3 = b ** 2 + (h + l) ** 2
+    s = min(s1, s2, s3)
+    return s
+
+
 def euler_086():
-    return 0
+    square_max = (10 ** 6) ** 2
+    squares = set([n * n for n in range(10**6)])
+
+    count = 0
+    m = 0
+    while True:
+        m += 1
+        cuboids = ((m, a, b)
+                   for a in range(1, m + 1)
+                   for b in range(1, a + 1))
+        for c in cuboids:
+            s = shortest_path_squared(*c)
+            if s in squares:
+                count += 1
+            if s > square_max:
+                raise Exception()
+        if count > 10 ** 6:
+            return m
 
 
 if __name__ == "__main__":
     solution = euler_086()
     print("e086.py: " + str(solution))
-    assert(solution == 0)
+    assert(solution == 1818)
+