## How to solve this mini?

Everything about Sudoku that doesn't fit in one of the other sections

### How to solve this mini?

Hi at all Sudoku experts,

I tried solving a 6x6 Sudoku and found a few numbers, the diagram looks like following then:

040005
506004
020500
005012
350200
000050

The "0's" are empty cells; can anyone help me by finding the next digit without "trial-and-error"?

Many thanks in advance,
Joe
sudokaku

Posts: 2
Joined: 20 December 2005

2s have to go in row 1 box 1 => must go in row 2 box 2.
emm

Posts: 987
Joined: 02 July 2005

Thank you em
But it was my mistake, this 2 I found as well (just forgot to fill it in) but the situation now is where I'm stuck!

Thanks,
Joe
sudokaku

Posts: 2
Joined: 20 December 2005

Do you know the little trick called Xwing - if a number is possible in only 2 cells in a column and only two cells in another column and those 4 cells also share the same 2 rows then you have an Xwing. It eliminates that number from any other cells that intersect with the corners of the X. It sounds complicated but it's actually beautifully simple.

In your example in columns 3 & 5 the number 3 can only go in rows 1 & 3. That's an x wing pattern and it lets you remove the 3s from r1c4 and r3c6.

Here are the places 3 can go in your grid - * marks the Xwing.

Code: Select all
` . . 3*| 3 3*. |   . 3 . | 3 . . |  -------+-------+ . . 3*| . 3*3 |   . 3 . | 3 . . |  -------+-------+ . . . | . . . |   . . . | 3 . 3 |  -------+-------+  `
emm

Posts: 987
Joined: 02 July 2005

sudokaku,

Please note that a 6x6 puzzle could divide into boxes of sizes 2x3 or 3x2 (which is why I prefer to categorize puzzles according to box size rather than grid size), i.e. your puzzle could be interpreted in two ways:

Code: Select all
`I. . 4 . | . . 5  5 . 6 | . . 4 -------+------  . 2 . | 5 . .  . . 5 | . 1 2 -------+------  3 5 . | 2 . .  . . . | . 5 . II. . 4 | . . | . 5  5 . | 6 . | . 4  . 2 | . 5 | . . -----+-----+----  . . | 5 . | 1 2  3 5 | . 2 | . .  . . | . . | 5 . `

Now, in the special case of your initial grid, we know it can't be II because that puzzle has no solutions, whereas Puzzle I has a unique solution, but in general it would help if you could indicate the box size used in any puzzle you post. Thanks.
rubylips

Posts: 149
Joined: 01 November 2005