Solve problem 142 and make 141 brute force work again.

python/e141.py

@@ -1,3 +1,4 @@
+import concurrent.futures
 from math import isqrt, gcd
 
 
@@ -6,14 +7,12 @@ def issqrt(n):
     return isq * isq == n
 
 
-def euler_141_brute_force():
-    import concurrent.futures
-
 def have_same_ratio(a, b, c, d):
     if b == 0 or d == 0:
         raise ValueError("Denominators must be non-zero")
     return a * d == b * c
 
+
 def check_range(start, end):
     local_sum = 0
     for i in range(start, end):
@@ -32,6 +31,8 @@ def euler_141_brute_force():
                 break
     return local_sum
 
+
+def euler_141_brute_force():
     s = 0
     m = 1_000_000
     range_size = 10_000
@@ -41,10 +42,8 @@ def euler_141_brute_force():
         for start in range(1, m, range_size):
             end = min(start + range_size, m)
             futures.append(executor.submit(check_range, start, end))
-
         for future in concurrent.futures.as_completed(futures):
             s += future.result()
-
     return s
 
 

python/e142.py

@@ -0,0 +1,38 @@
+from math import isqrt
+
+
+def iq(n):
+    isq = isqrt(n)
+    return isq * isq == n
+
+
+def euler_142():
+    # x + y x - y x + z x - z y + z y - z
+    NMAX = 1_000_000
+    squares = [n * n for n in range(1, NMAX)]
+    for x in range(1, NMAX):
+        for s1 in squares:
+            y = x - s1 # s1 = x - y
+            if y <= 0:
+                break
+            if not iq(x + y): # s2 = x + y
+                continue
+            for s3 in squares:
+                z = y - s3 # s3 = y - z
+                if x - z <= 0:
+                    continue
+                if z <= 0:
+                    break
+                if not iq(y + z): # s4 = y + z
+                    continue
+                if iq(x + z) and iq(x - z):
+                    print(x, y, z, x + y + z)
+                    return x + y + z
+    return None
+
+
+if __name__ == "__main__":
+    solution = euler_142()
+    print("e142.py: " + str(solution))
+    assert solution == 1006193
+