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
 
 
@@ -6,32 +7,32 @@ def issqrt(n):
     return isq * isq == n
 
 
+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):
+        if i % 10000 == 0:
+            print(i)
+        n = i * i
+        for d in range(1, i):
+            q = n // d
+            r = n % d
+            if r == 0:
+                continue
+            assert r < d and d < q
+            if have_same_ratio(d, r, q, d):
+                print(f"{n=} {i=} {r=} {d=} {q=}")
+                local_sum += n
+                break
+    return local_sum
+
+
 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):
-            if i % 10000 == 0:
-                print(i)
-            n = i * i
-            for d in range(1, i):
-                q = n // d
-                r = n % d
-                if r == 0:
-                    continue
-                assert r < d and d < q
-                if have_same_ratio(d, r, q, d):
-                    print(f"{n=} {i=} {r=} {d=} {q=}")
-                    local_sum += n
-                    break
-        return local_sum
-
     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
+