guardian_clueless_sudoku.py

from collections import Counter
from pprint import pprint

BOARD = """
a a a a b
c c c a b
d d c b b
d e c c c
d e e e c
""".strip().splitlines()

BOARD = [s.strip().split() for s in BOARD]

BLOCKS = {}

for y, line in enumerate(BOARD):
    for x, c in enumerate(line):
        BLOCKS.setdefault(c, [])
        BLOCKS[c].append((x, y))

def debug():
    for k, block in BLOCKS.items():
        print()
        print(k)
        for x, y in block:
            print(x, y, BOARD[y][x])

board = [[None] * 5 for _ in range(5)]

def row(y):
    return [(x, y) for x in range(5)]

def column(x):
    return [(x, y) for y in range(5)]

def unique(blocks):
    d = Counter(board[y][x] for x, y in blocks)
    del d[None]
    return all(v == 1 for v in d.values())

def shape(i):
    return list(BLOCKS.values())[i]

def total(blocks):
    low = sum(board[y][x] or 1 for x, y in blocks)
    high = sum(board[y][x] or 5 for x, y in blocks)
    return low <= 15 <= high

def check():
    return all(
        unique(row(i)) and
        total(row(i)) and
        unique(column(i)) and
        total(column(i)) and
        total(shape(i)) for i in range(5))

INDICES = tuple((x, y) for x in range(5) for y in range(5))

def recur(indices):
    if not indices:
        return solution()

    x, y = indices[0]
    for v in range(1, 6):
        board[y][x] = v
        if check():
            recur(indices[1:])

    board[y][x] = None

def solution():
    assert all(board[y][x] is not None for x in range(5) for y in range(5))
    pprint(board)


recur(INDICES)

Generates a single result:

[[1, 3, 4, 2, 5],
 [4, 1, 2, 5, 3],
 [2, 5, 1, 3, 4],
 [5, 4, 3, 1, 2],
 [3, 2, 5, 4, 1]]