From 7efb4fb78f6765307066b7647ae3aef4920155d7 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Wed, 21 Apr 2021 21:53:35 -0400
Subject: [PATCH] Solve problem 90

---
 python/e090.py | 64 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 python/e090.py

diff --git a/python/e090.py b/python/e090.py
new file mode 100644
index 0000000..87c33fb
--- /dev/null
+++ b/python/e090.py
@@ -0,0 +1,64 @@
+#
+def choose(xs, n):
+    """
+    Computes r choose n, in other words choose n from xs.
+    Returns combinations and not permutations.
+    """
+
+    if not xs or n == 0:
+        return [[]]
+    if len(xs) == n:
+        return [xs]
+
+    rs = []
+    x = xs[0]
+    for r in choose(xs[1:], n - 1):
+        rs.append([x] + r)
+    for r in choose(xs[1:], n):
+        rs.append(r)
+    return rs
+
+
+def pairs(xs):
+    if len(xs) == 2:
+        return [xs]
+    r = []
+    a = xs[0]
+    for b in xs[1:]:
+        r.append([a, b])
+
+    return r + pairs(xs[1:])
+
+
+def can_form_squares(pair):
+    xs, ys = pair
+
+    # replace 9s with 6s
+    for d, e in [(0, 1), (0, 4), (0, 6), (1, 6),
+                 (2, 5), (3, 6), (4, 6), (6, 4), (8, 1)]:
+        if d in xs and e in ys:
+            continue
+        elif e in xs and d in ys:
+            continue
+        return False
+    return True
+
+
+def euler_090():
+    # replace 9s with 6s to handle "up-side down usage of 6" without hassle
+    xs = list(range(0, 9)) + [6]
+
+    cs = choose(xs, 6)
+    ps = pairs(cs)
+    count = 0
+    for p in ps:
+        if can_form_squares(p):
+            count += 1
+    return count
+
+
+if __name__ == "__main__":
+    solution = euler_090()
+    print("e090.py: " + str(solution))
+    assert(solution == 1217)
+