Solve p51 in python (82nd solved!)

README.rst

@@ -107,7 +107,7 @@ Olivia's Project Euler Solutions
    |            |                            |        | |Lu-Cov| |br|     |
    |            |                            |        | |LuaCheck|        |
    +------------+----------------------------+--------+-------------------+
-   | Python     | CPython 3.6+ |br|          | 81     | |Python| |br|     |
+   | Python     | CPython 3.6+ |br|          | 82     | |Python| |br|     |
    |            | Pypy 3.6+ |br|             |        | |Py-Cov| |br|     |
    |            | GraalPy 23.1+ |br|         |        | |CodeQL| |br|     |
    |            | Browser [#]_               |        | |PythonLint|      |

_data/answers.tsv

@@ -49,6 +49,7 @@ ID	type	size	answer
 48	int	64	9110846700
 49	int	64	296962999629
 50	int	32	997651
+51	int	32 	121313
 52	int	32	142857
 53	int	16	4075
 55	uint	8	249

docs/index.rst

@@ -178,6 +178,8 @@ Problems Solved
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`050`|           |            |            |            |            |            |            |:py-d:`0050`|            |
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
+  |:prob:`051`|           |            |            |            |            |            |            |:py-d:`0051`|            |
+  +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`052`|           |            |            |            |            |            |            |:py-d:`0052`|            |
   +-----------+-----------+------------+------------+------------+------------+------------+------------+------------+------------+
   |:prob:`053`|           |            |            |            |            |            |            |:py-d:`0053`|:rs-d:`0053`|

docs/src/python/p0051.rst

@@ -0,0 +1,25 @@
+Python Implementation of Problem 51
+===================================
+
+View source code :source:`python/src/p0051.py`
+
+Includes
+--------
+
+- :py:func:`~python.src.lib.primes.is_prime`
+- :external:py:func:`itertools.combinations`
+- :external:py:func:`itertools.count`
+- :external:py:func:`itertools.product`
+
+Problem Solution
+----------------
+
+.. automodule:: python.src.p0051
+   :members:
+   :undoc-members:
+
+.. literalinclude:: ../../../python/src/p0051.py
+   :language: python
+   :linenos:
+
+.. tags:: prime-number, digit-manipulation

python/README.rst

@@ -177,6 +177,7 @@ Problems Solved
 -  ☒ `48 <./src/p0048.py>`__
 -  ☒ `49 <./src/p0049.py>`__
 -  ☒ `50 <./src/p0050.py>`__
+-  ☒ `51 <./src/p0051.py>`__
 -  ☒ `52 <./src/p0052.py>`__
 -  ☒ `53 <./src/p0053.py>`__
 -  ☒ `55 <./src/p0055.py>`__

python/src/p0051.py

@@ -0,0 +1,64 @@
+"""
+Project Euler Problem 51
+
+Again, surprised how effective the brute force solution was
+
+Problem:
+
+By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53,
+73, and 83, are all prime.
+
+By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven
+primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993.
+Consequently 56003, being the first member of this family, is the smallest prime with this property.
+
+Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit,
+is part of an eight prime value family.
+"""
+from itertools import combinations, count, product
+from typing import List, Tuple
+
+from .lib.primes import is_prime
+
+all_digits = tuple(str(x) for x in range(10))
+non_zero = all_digits[1:]
+endings = ("1", "3", "7", "9")
+
+
+def main() -> int:
+    for L in count(5):
+        largest_possible: int = 10**L
+        for Ls in range(1, L - 1):
+            for indices in combinations(range(L - 1), Ls):
+                mask = ["d"] * L  # d can be replaced by any digit
+                for index in indices:
+                    mask[index] = "s"  # s can be replaced by any single digit
+                valid, smallest = check_mask(mask, largest_possible, L, Ls)
+                if valid:
+                    return smallest
+    return -1  # pragma: no cover
+
+
+def check_mask(mask: List[str], largest_possible: int, L: int, Ls: int) -> Tuple[bool, int]:
+    for start, middle, end in product(non_zero, product(all_digits, repeat=(L - Ls - 2)), endings):
+        digits = (start, *middle, end)
+        current = mask.copy()
+        for digit in digits:
+            current[current.index("d")] = digit
+        valid = 0
+        smallest = largest_possible
+        if current[0] == "s":
+            selection = non_zero
+        else:
+            selection = all_digits
+        for s in selection:
+            new = [x if x != "s" else s for x in current]
+            num = int("".join(new))
+            if is_prime(num):
+                valid += 1
+                smallest = min(smallest, num)
+            elif 10 - int(s) + valid <= 8:
+                break
+        else:
+            return True, smallest
+    return False, 0

python/test_euler.py

@@ -19,9 +19,7 @@
 
 answers: Dict[int, Union[int, str]] = {
     x: get_answer(x) for x in (
-        *range(1, 51),
-        52,
-        53,
+        *range(1, 54),
         *range(55, 61),
         63,
         67,