From 642432cef87263e19facf84f25c0eb1bdbbf6a91 Mon Sep 17 00:00:00 2001
From: felixm <mail@felixm.de>
Date: Sat, 13 Apr 2024 18:31:32 -0400
Subject: [PATCH] Solve problem 151.

---
 python/e151.py | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 python/e151.py

diff --git a/python/e151.py b/python/e151.py
new file mode 100644
index 0000000..34a289f
--- /dev/null
+++ b/python/e151.py
@@ -0,0 +1,31 @@
+from fractions import Fraction
+from functools import lru_cache
+
+
+@lru_cache
+def expected_singles(sheets):
+    count = 0
+    if len(sheets) == 1 and sheets[0] == 5:
+        return 0
+    elif len(sheets) == 1:
+        count += 1
+
+    weight = Fraction(1, len(sheets))
+    for sheet in sheets:
+        nsheets = list(sheets)
+        nsheets.remove(sheet)
+        for nsheet in range(sheet, 5):
+            nsheets.append(nsheet + 1)
+        count += weight * expected_singles(tuple(sorted(nsheets)))
+    return count
+
+
+def euler_151():
+    return round(float(expected_singles(tuple([2, 3, 4, 5]))), 6)
+
+
+if __name__ == "__main__":
+    solution = euler_151()
+    print("e151.py: " + str(solution))
+    assert(solution == 0.464399)
+