Разработка, JFF

Судоку

Мне тут попалось судоку, которое я не мог решить без полного перебора вариантов. Когда было сделано несколько итераций, то стало понятно, что решения можно найти лишь перебирая все варианты. Нельзя было найти ни одной подсказки.

Вот оно:

7 4 5
6 8 9
4
9 5 6 7
2 7 3
6 3
3 1
3 8
4 8 6

Стало интересно: может быть где-то ошибка в поиске решения? Все же человек не машина, а следовательно ошибается чаще.

Что мы знаем про простейшие решения судоку?

Исходники


Знаем мы несколько паттернов:

  • В одной ячейке не может быть повторяющихся чисел
  • В строке или столбце так же не может быть повторяющихся чисел

Есть еще одно правило, которое можно пронаблюдать на примере.

Формулируется следующим образом:

  • Если в одной малой таблице некоторое число может быть только в одном столбце или одной строке, то эта строка (столбец) в других малых таблицах не может содержать это число

Непонятно. Да. Непонятно. Но всегда можно посмотреть на примере.

Разместим все возможные варианты цифры 5

7 4 5
5 5 6 8 9
5 5 5 5 4
9 5 6 7
2 5 5 7 5 3
6 3 5 5 5 5 5
3 5 1 5 5 5 5 5
5 5 3 5 5 8 5
4 5 8 5 5 6 5

Очевидно, что пятерки, которые помечены красным существовать не могут.

Что в итоге? Напишем программу, которая пользуется вышеприведенными аксиомами и увидим, что иногда без полного перепора судоку не решается.🙂

Вывод приложения:

before scan
[0, 7, 0, 0, 0, 0, 4, 0, 5]
[0, 0, 0, 6, 8, 9, 0, 0, 0]
[0, 0, 0, 0, 0, 4, 0, 0, 0]
[9, 0, 5, 0, 6, 0, 0, 0, 7]
[0, 2, 0, 0, 0, 7, 0, 3, 0]
[6, 3, 0, 0, 0, 0, 0, 0, 0]
[3, 0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 3, 0, 0, 8, 0, 0]
[4, 0, 0, 8, 0, 0, 6, 0, 0]
suggest for board
[[1, 2, 8], 7, [2, 3, 6, 8, 9], [1, 2], [1, 2, 3], [1, 2], 4, [1, 2, 6, 8, 9], 5]
[[1, 2, 5], [1, 4, 5], [2, 3, 4], 6, 8, 9, [1, 2, 3, 7], [1, 2, 7], [1, 2]]
[[1, 2, 8], [1, 6, 9], [2, 3, 6, 8, 9], [1, 2, 5, 7], [1, 2, 3, 5, 7], 4, [1, 2, 3, 9], [1, 2, 6, 8, 9], [1, 2, 8, 9]]
[9, [1, 4], 5, [1, 2, 4], 6, [1, 2, 3, 8], [1, 2], [1, 2, 4, 8], 7]
[[1, 8], 2, [4, 8], [1, 4, 5, 9], [1, 4, 5, 9], 7, [1, 5, 9], 3, [1, 4, 6, 8, 9]]
[6, 3, [4, 7, 8], [1, 2, 4, 5, 9], [1, 2, 4, 5, 9], [1, 2, 5, 8], [1, 2, 5, 9], [1, 2, 4, 5, 8, 9], [1, 2, 4, 8, 9]]
[3, [5, 6, 8, 9], 1, [2, 4, 5, 7, 9], [2, 4, 5, 7, 9], [2, 5, 6], [2, 5, 7, 9], [2, 4, 5, 7, 9], [2, 4, 9]]
[[2, 5, 7], [5, 6, 9], [2, 6, 9], 3, [1, 2, 4, 5, 9], [1, 2, 5, 6], 8, [1, 2, 4, 5, 9], [1, 2, 4, 9]]
[4, [5, 9], [2, 9], 8, [1, 2, 5, 7, 9], [1, 2, 5], 6, [1, 2, 5, 7, 9], [1, 2, 3, 9]]

description
[((5, 2), 7), ((3, 5), 3), ((4, 8), 6), ((7, 0), 7), ((6, 1), 8), ((8, 8), 3)]
after solve
[0, 7, 0, 0, 0, 0, 4, 0, 5]
[0, 0, 0, 6, 8, 9, 0, 0, 0]
[0, 0, 0, 0, 0, 4, 0, 0, 0]
[9, 0, 5, 0, 6, 3, 0, 0, 7]
[0, 2, 0, 0, 0, 7, 0, 3, 6]
[6, 3, 7, 0, 0, 0, 0, 0, 0]
[3, 8, 1, 0, 0, 0, 0, 0, 0]
[7, 0, 0, 3, 0, 0, 8, 0, 0]
[4, 0, 0, 8, 0, 0, 6, 0, 3]
before scan
[0, 7, 0, 0, 0, 0, 4, 0, 5]
[0, 0, 0, 6, 8, 9, 0, 0, 0]
[0, 0, 0, 0, 0, 4, 0, 0, 0]
[9, 0, 5, 0, 6, 3, 0, 0, 7]
[0, 2, 0, 0, 0, 7, 0, 3, 6]
[6, 3, 7, 0, 0, 0, 0, 0, 0]
[3, 8, 1, 0, 0, 0, 0, 0, 0]
[7, 0, 0, 3, 0, 0, 8, 0, 0]
[4, 0, 0, 8, 0, 0, 6, 0, 3]
suggest for board
[[1, 2, 8], 7, [3, 6, 8, 9], [1, 2], [1, 2, 3], [1, 2], 4, [1, 2, 6, 9], 5]
[[1, 2, 5], [1, 4], [3, 4], 6, 8, 9, [1, 2, 3, 7], [1, 2, 7], [1, 2]]
[[1, 2, 8], [1, 6, 9], [3, 6, 8, 9], [1, 2, 5, 7], [1, 2, 3, 5, 7], 4, [1, 2, 3, 9], [1, 2, 6, 9], [1, 2, 8, 9]]
[9, [1, 4], 5, [1, 2, 4], 6, 3, [1, 2], [1, 2, 4, 8], 7]
[[1, 8], 2, [4, 8], [1, 4, 5, 9], [1, 4, 5, 9], 7, [1, 5, 9], 3, 6]
[6, 3, 7, [1, 2, 4, 5, 9], [1, 2, 4, 5, 9], [1, 2, 5, 8], [1, 2, 5, 9], [1, 2, 4, 5, 9], [1, 2, 4, 9]]
[3, 8, 1, [2, 4, 5, 7, 9], [2, 4, 5, 7, 9], [2, 5, 6], [2, 5, 7, 9], [2, 4, 5, 7, 9], [2, 4, 9]]
[7, [5, 6, 9], [2, 6, 9], 3, [1, 2, 4, 5, 9], [1, 2, 5], 8, [1, 2, 4, 5, 9], [1, 2, 4, 9]]
[4, [5, 9], [2, 9], 8, [1, 2, 5, 7, 9], [1, 2, 5], 6, [1, 2, 5, 7, 9], 3]

description
[((1, 0), 5), ((2, 8), 8), ((5, 5), 8), ((3, 7), 8), ((6, 5), 6)]
after solve
[0, 7, 0, 0, 0, 0, 4, 0, 5]
[5, 0, 0, 6, 8, 9, 0, 0, 0]
[0, 0, 0, 0, 0, 4, 0, 0, 8]
[9, 0, 5, 0, 6, 3, 0, 8, 7]
[0, 2, 0, 0, 0, 7, 0, 3, 6]
[6, 3, 7, 0, 0, 8, 0, 0, 0]
[3, 8, 1, 0, 0, 6, 0, 0, 0]
[7, 0, 0, 3, 0, 0, 8, 0, 0]
[4, 0, 0, 8, 0, 0, 6, 0, 3]
before scan
[0, 7, 0, 0, 0, 0, 4, 0, 5]
[5, 0, 0, 6, 8, 9, 0, 0, 0]
[0, 0, 0, 0, 0, 4, 0, 0, 8]
[9, 0, 5, 0, 6, 3, 0, 8, 7]
[0, 2, 0, 0, 0, 7, 0, 3, 6]
[6, 3, 7, 0, 0, 8, 0, 0, 0]
[3, 8, 1, 0, 0, 6, 0, 0, 0]
[7, 0, 0, 3, 0, 0, 8, 0, 0]
[4, 0, 0, 8, 0, 0, 6, 0, 3]
suggest for board
[[1, 2, 8], 7, [3, 6, 8, 9], [1, 2], [1, 2, 3], [1, 2], 4, [1, 2, 6, 9], 5]
[5, [1, 4], [3, 4], 6, 8, 9, [1, 2, 3, 7], [1, 2, 7], [1, 2]]
[[1, 2], [1, 6, 9], [3, 6, 9], [1, 2, 5, 7], [1, 2, 3, 5, 7], 4, [1, 2, 3, 9], [1, 2, 6, 9], 8]
[9, [1, 4], 5, [1, 2, 4], 6, 3, [1, 2], 8, 7]
[[1, 8], 2, [4, 8], [1, 4, 5, 9], [1, 4, 5, 9], 7, [1, 5, 9], 3, 6]
[6, 3, 7, [1, 2, 5, 9], [1, 2, 5, 9], 8, [1, 2, 5, 9], [1, 2, 4, 5, 9], [1, 2, 4, 9]]
[3, 8, 1, [2, 4, 5, 7, 9], [2, 4, 5, 7, 9], 6, [2, 5, 7, 9], [2, 4, 5, 7, 9], [2, 4, 9]]
[7, [5, 6, 9], [2, 6, 9], 3, [1, 2, 4, 5, 9], [1, 2, 5], 8, [1, 2, 4, 5, 9], [1, 2, 4, 9]]
[4, [5, 9], [2, 9], 8, [1, 2, 5, 7, 9], [1, 2, 5], 6, [1, 2, 5, 7, 9], 3]

description
[]
Sorry. couldn't solve this

На месте пустых (они же нулевые) значений печатается подсказка по тому, какой элемент может быть на этом месте.

Description — это список подстановок элемента с индексами в базовой матрице.

И конечно решение на другом примере.

before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[0, 0, 7, 0, 0, 0, 9, 1, 0]
[2, 0, 0, 0, 5, 4, 0, 0, 0]
[0, 8, 0, 0, 0, 0, 6, 3, 0]
[0, 0, 0, 6, 0, 0, 1, 8, 0]
[0, 2, 0, 3, 0, 0, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 0, 0, 0, 0, 0]
suggest for board
[[1, 3, 8, 9], [1, 3, 9], 5, [1, 2, 7, 8, 9], 6, [1, 3, 7, 9], [2, 4, 7, 8], [2, 4, 7], [3, 7, 8]]
[[3, 4, 8], [3, 4, 6], 7, [2, 8], [2, 3], [3], 9, 1, [3, 5, 6, 8]]
[2, [1, 3, 6, 9], [1, 3, 8], [1, 7, 8, 9], 5, 4, [7, 8], [6, 7], [3, 6, 7, 8]]
[[1, 4, 5, 9], 8, [1, 4], [1, 2, 4, 5, 7, 9], [1, 2, 4, 7, 9], [1, 5, 7, 9], 6, 3, [2, 7, 9]]
[[3, 4, 5, 9], [3, 4, 5, 7, 9], [3, 4], 6, [2, 4, 9], [5, 9], 1, 8, [2, 9]]
[[1, 9], 2, [1, 6], 3, [1, 7, 9], [1, 7, 8, 9], [4, 5, 7], [4, 5, 7, 9], [7, 9]]
[6, [1, 3, 4, 5], [1, 3, 4], [1, 4, 5, 7, 9], 8, 2, [5, 7], [5, 7, 9], [1, 7, 9]]
[[1, 5, 8], [1, 5], [1, 2, 8], [1, 5, 7, 9], [1, 7, 9], [1, 5, 6, 7, 9], 3, [5, 6, 7, 9], 4]
[7, [1, 4, 5], 9, [1, 4, 5], [1, 3, 4], [1, 3, 5, 6], [2, 5, 8], [2, 5, 6], [1, 6, 8]]

description
[((1, 5), 3), ((1, 8), 5), ((5, 2), 6), ((4, 1), 7), ((5, 5), 8), ((7, 2), 2)]
after solve
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[0, 0, 7, 0, 0, 3, 9, 1, 5]
[2, 0, 0, 0, 5, 4, 0, 0, 0]
[0, 8, 0, 0, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 0]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[0, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 0, 0, 0, 0, 0]
before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[0, 0, 7, 0, 0, 3, 9, 1, 5]
[2, 0, 0, 0, 5, 4, 0, 0, 0]
[0, 8, 0, 0, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 0]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[0, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 0, 0, 0, 0, 0]
suggest for board
[[1, 3], [1, 3, 9], 5, [1, 7, 8, 9], 6, [1, 7, 9], [2, 4, 7, 8], [2, 4, 7], [3, 7, 8]]
[[4], [4, 6], 7, [2, 8], [2], 3, 9, 1, 5]
[2, [1, 3, 9], [1, 3, 8], [1, 7, 8, 9], 5, 4, [7, 8], [6, 7], [3, 6, 7, 8]]
[[1, 4, 5, 9], 8, [1, 4], [1, 2, 4, 5, 7, 9], [1, 2, 4, 7, 9], [1, 5, 7, 9], 6, 3, [2, 7, 9]]
[[3, 4, 5, 9], 7, [3, 4], 6, [2, 4, 9], [5, 9], 1, 8, [2, 9]]
[[1, 9], 2, 6, 3, [1, 7, 9], 8, [4, 5, 7], [4, 5, 7, 9], [7, 9]]
[6, [1, 3, 4, 5], [1, 3, 4], [1, 4, 5, 7, 9], 8, 2, [5, 7], [5, 7, 9], [1, 7, 9]]
[[1, 8], [1, 5], 2, [1, 5, 7, 9], [1, 7, 9], [1, 5, 6, 7, 9], 3, [5, 6, 7, 9], 4]
[7, [1, 4, 5], 9, [1, 4, 5], [1, 3, 4], [1, 5, 6], [2, 5, 8], [2, 5, 6], [1, 6, 8]]

description
[((1, 0), 4), ((1, 1), 6), ((2, 2), 8), ((1, 4), 2), ((7, 0), 8), ((8, 4), 3)]
after solve
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 0, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 0, 0, 0]
[0, 8, 0, 0, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 0]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 0, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 0, 0, 0]
[0, 8, 0, 0, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 0]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
suggest for board
[[1, 3], [1, 3, 9], 5, [1, 7, 9], 6, [1, 7, 9], [2, 4, 7, 8], [2, 4, 7], [3, 7, 8]]
[4, 6, 7, [8], 2, 3, 9, 1, 5]
[2, [1, 3, 9], 8, [1, 7, 9], 5, 4, [7], [6, 7], [3, 6, 7]]
[[1, 5, 9], 8, [1, 4], [1, 2, 5, 7, 9], [1, 4, 7, 9], [1, 5, 7, 9], 6, 3, [7, 9]]
[[3, 5, 9], 7, [3, 4], 6, [4, 9], [5, 9], 1, 8, [2, 9]]
[[1, 9], 2, 6, 3, [1, 7, 9], 8, [4, 5, 7], [4, 5, 7, 9], [7, 9]]
[6, [1, 3, 4, 5], [1, 3], [1, 4, 5, 7, 9], 8, 2, [5, 7], [5, 7, 9], [1, 7, 9]]
[8, [1, 5], 2, [1, 5, 7, 9], [1, 7, 9], [1, 5, 6, 7, 9], 3, [5, 6, 7, 9], 4]
[7, [1, 4, 5], 9, [1, 4, 5], 3, [1, 5, 6], [2, 5, 8], [2, 5, 6], [1, 6, 8]]

description
[((1, 3), 8), ((1, 3), 8), ((2, 6), 7), ((3, 3), 2), ((4, 8), 2)]
after solve
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 0, 0]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 0, 0]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 0, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
suggest for board
[[1, 3], [1, 3, 9], 5, [1, 7, 9], 6, [1, 7, 9], [2, 4, 8], [2, 4], [3, 8]]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, [1, 3, 9], 8, [1, 9], 5, 4, 7, [6], [3, 6]]
[[1, 5, 9], 8, [1, 4], 2, [1, 4, 7, 9], [1, 5, 7, 9], 6, 3, [7, 9]]
[[3, 5, 9], 7, [3, 4], 6, [4, 9], [5, 9], 1, 8, 2]
[[1, 9], 2, 6, 3, [1, 7, 9], 8, [4, 5], [4, 5, 7, 9], [7, 9]]
[6, [1, 3, 4, 5], [1, 3], [1, 4, 5, 7, 9], 8, 2, [5], [5, 7, 9], [1, 7, 9]]
[8, [1, 5], 2, [1, 5, 7, 9], [1, 7, 9], [1, 6, 7, 9], 3, [5, 6, 7, 9], 4]
[7, [1, 4, 5], 9, [1, 4, 5], 3, [1, 6], [2, 5, 8], [2, 5, 6], [1, 6, 8]]

description
[((2, 7), 6), ((6, 6), 5)]
after solve
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 0]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 5, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 0]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 0, 0, 0]
[6, 0, 0, 0, 8, 2, 5, 0, 0]
[8, 0, 2, 0, 0, 0, 3, 0, 4]
[7, 0, 9, 0, 3, 0, 0, 0, 0]
suggest for board
[[1, 3], [1, 3, 9], 5, [1, 7, 9], 6, [1, 7, 9], [2, 4, 8], [2, 4], [3, 8]]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, [1, 3, 9], 8, [1, 9], 5, 4, 7, 6, [3]]
[[1, 5, 9], 8, [1, 4], 2, [1, 4, 7, 9], [1, 5, 7, 9], 6, 3, [7, 9]]
[[3, 5, 9], 7, [3, 4], 6, [4, 9], [5, 9], 1, 8, 2]
[[1, 9], 2, 6, 3, [1, 7, 9], 8, [4], [4, 5, 7, 9], [7, 9]]
[6, [1, 3, 4], [1, 3], [1, 4, 7, 9], 8, 2, 5, [7, 9], [1, 7, 9]]
[8, [1, 5], 2, [1, 5, 7, 9], [1, 7, 9], [1, 6, 7, 9], 3, [7, 9], 4]
[7, [1, 4, 5], 9, [1, 4, 5], 3, [1], [2, 8], [2], [1, 6, 8]]

description
[((2, 8), 3), ((5, 6), 4), ((5, 7), 5), ((8, 5), 1), ((7, 5), 6), ((8, 7), 2), ((8, 8), 6)]
after solve
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 3]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 4, 5, 0]
[6, 0, 0, 0, 8, 2, 5, 0, 0]
[8, 0, 2, 0, 0, 6, 3, 0, 4]
[7, 0, 9, 0, 3, 1, 0, 2, 6]
before scan
[0, 0, 5, 0, 6, 0, 0, 0, 0]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 3]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 4, 5, 0]
[6, 0, 0, 0, 8, 2, 5, 0, 0]
[8, 0, 2, 0, 0, 6, 3, 0, 4]
[7, 0, 9, 0, 3, 1, 0, 2, 6]
suggest for board
[[1, 3], [1, 3, 9], 5, [1, 7, 9], 6, [7, 9], [2], [4], [8]]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, [1, 9], 8, [1, 9], 5, 4, 7, 6, 3]
[[1, 5, 9], 8, [1, 4], 2, [1, 4, 7, 9], [5, 7, 9], 6, 3, [7, 9]]
[[3, 5, 9], 7, [3, 4], 6, [4, 9], [5, 9], 1, 8, 2]
[[1, 9], 2, 6, 3, [1, 7, 9], 8, 4, 5, [7, 9]]
[6, [3, 4], [3], [4, 7, 9], 8, 2, 5, [7, 9], [1]]
[8, [1, 5], 2, [5, 7, 9], [7, 9], 6, 3, [7, 9], 4]
[7, [4, 5], 9, [4, 5], 3, 1, [8], 2, 6]

description
[((0, 8), 8), ((0, 6), 2), ((0, 7), 4), ((0, 8), 8), ((0, 6), 2), ((0, 7), 4), ((6, 2), 3), ((7, 1), 1), ((8, 6), 8), ((6, 8), 1), ((8, 6), 8), ((6, 8), 1)]
after solve
[0, 0, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 3]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 4, 5, 0]
[6, 0, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 0, 0, 6, 3, 0, 4]
[7, 0, 9, 0, 3, 1, 8, 2, 6]
before scan
[0, 0, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 0, 8, 0, 5, 4, 7, 6, 3]
[0, 8, 0, 2, 0, 0, 6, 3, 0]
[0, 7, 0, 6, 0, 0, 1, 8, 2]
[0, 2, 6, 3, 0, 8, 4, 5, 0]
[6, 0, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 0, 0, 6, 3, 0, 4]
[7, 0, 9, 0, 3, 1, 8, 2, 6]
suggest for board
[[1], [3, 9], 5, [7, 9], 6, [7, 9], 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, [9], 8, [1, 9], 5, 4, 7, 6, 3]
[[5, 9], 8, [1, 4], 2, [4, 7, 9], [5, 7, 9], 6, 3, [7, 9]]
[[3, 5, 9], 7, [4], 6, [4, 9], [5, 9], 1, 8, 2]
[[9], 2, 6, 3, [1, 7, 9], 8, 4, 5, [7, 9]]
[6, [4], 3, [4, 7, 9], 8, 2, 5, [7, 9], 1]
[8, 1, 2, [5, 7, 9], [7, 9], 6, 3, [7, 9], 4]
[7, [4, 5], 9, [4], 3, 1, 8, 2, 6]

description
[((0, 0), 1), ((2, 1), 9), ((0, 0), 1), ((0, 1), 3), ((2, 3), 1), ((5, 0), 9), ((4, 2), 4), ((4, 0), 3), ((3, 2), 1), ((5, 4), 1), ((6, 1), 4), ((8, 1), 5), ((8, 3), 4), ((7, 3), 5)]
after solve
[1, 3, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[0, 8, 1, 2, 0, 0, 6, 3, 0]
[3, 7, 4, 6, 0, 0, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 0]
[6, 4, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 5, 0, 6, 3, 0, 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]
before scan
[1, 3, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[0, 8, 1, 2, 0, 0, 6, 3, 0]
[3, 7, 4, 6, 0, 0, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 0]
[6, 4, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 5, 0, 6, 3, 0, 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]
suggest for board
[1, 3, 5, [7, 9], 6, [7, 9], 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[[5], 8, 1, 2, [4, 7], [7], 6, 3, [9]]
[3, 7, 4, 6, [9], [5, 9], 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, [7]]
[6, 4, 3, [7, 9], 8, 2, 5, [7, 9], 1]
[8, 1, 2, 5, [7, 9], 6, 3, [7, 9], 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]

description
[((3, 0), 5), ((3, 0), 5), ((4, 4), 9), ((3, 5), 7), ((3, 4), 4), ((4, 5), 5), ((3, 8), 9), ((5, 8), 7), ((3, 8), 9), ((5, 8), 7)]
after solve
[1, 3, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[5, 8, 1, 2, 4, 7, 6, 3, 9]
[3, 7, 4, 6, 9, 5, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 7]
[6, 4, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 5, 0, 6, 3, 0, 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]
before scan
[1, 3, 5, 0, 6, 0, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[5, 8, 1, 2, 4, 7, 6, 3, 9]
[3, 7, 4, 6, 9, 5, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 7]
[6, 4, 3, 0, 8, 2, 5, 0, 1]
[8, 1, 2, 5, 0, 6, 3, 0, 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]
suggest for board
[1, 3, 5, [7], 6, [9], 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[5, 8, 1, 2, 4, 7, 6, 3, 9]
[3, 7, 4, 6, 9, 5, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 7]
[6, 4, 3, [9], 8, 2, 5, [7], 1]
[8, 1, 2, 5, [7], 6, 3, [9], 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]

description
[((0, 5), 9), ((0, 3), 7), ((0, 5), 9), ((0, 3), 7), ((6, 3), 9), ((7, 4), 7), ((6, 3), 9), ((7, 4), 7), ((7, 7), 9), ((6, 7), 7), ((7, 7), 9), ((6, 7), 7)]
after solve
[1, 3, 5, 7, 6, 9, 2, 4, 8]
[4, 6, 7, 8, 2, 3, 9, 1, 5]
[2, 9, 8, 1, 5, 4, 7, 6, 3]
[5, 8, 1, 2, 4, 7, 6, 3, 9]
[3, 7, 4, 6, 9, 5, 1, 8, 2]
[9, 2, 6, 3, 1, 8, 4, 5, 7]
[6, 4, 3, 9, 8, 2, 5, 7, 1]
[8, 1, 2, 5, 7, 6, 3, 9, 4]
[7, 5, 9, 4, 3, 1, 8, 2, 6]

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