Sudoku Players' Forum (clone)

First, this isn't a Sudoku puzzle, but I think that it is similar. I've been trying to finish it, but I'm not smart enough. So, I found this forum and figured someone on here is probably smart enough to figure it out. It's been driving me crazy. Have a look at it please. (see attached image)

Each row must contain one of each number which means each number must be ommitted once only.
We can therefore compose an 8th row containing the ommitted numbers out of the 8 valid ones for each column.
Now try a methodical method of diagonally placing each number in the other 7 columns where it must appear.

Here's a connection with 12x12 Sudokus:

Code: Select all

+---------++---------+---------+
| 1 2 3 4 || x x x x | x x x - | Set 1
| 5 6 7 8 || x x x x | x x x - | Set 2
| 9 a b c || x x x x | x x x - | Set 3
+---------++---------+---------+
| 2 3 4 1 || x x x x | x x x - | Set 1
| 6 7 8 5 || x x x x | x x x - | Set 2
| a b c 9 || x x x x | x x x - | Set 3
+---------++---------+---------+
| 3 4 1 2 || x x x x | x x x - | Set 1
| 7 8 5 6 || x x x x | x x x - | Set 2
| b c 9 a || x x x x | x x x - | Set 3
+---------++---------+---------+
| 4 1 2 3 || x x x x | x x x - | Set 1
| 8 5 6 7 || x x x x | x x x - | Set 2
| c 9 a b || x x x x | x x x - | Set 3
+---------++---------+---------+

You can get one solution from this grid:

Code: Select all

+---------++---------+---------+
| 1 2 3 4 || 5 6 7 8 | 9 a b c | Set 1
| 5 6 7 8 || 9 a b c | 1 2 3 4 | Set 2
| 9 a b c || 1 2 3 4 | 5 6 7 8 | Set 3
+---------++---------+---------+
| 2 3 4 1 || 6 7 8 5 | a b c 9 | Set 1
| 6 7 8 5 || a b c 9 | 2 3 4 1 | Set 2
| a b c 9 || 2 3 4 1 | 6 7 8 5 | Set 3
+---------++---------+---------+
| 3 4 1 2 || 7 8 5 6 | b c 9 a | Set 1
| 7 8 5 6 || b c 9 a | 3 4 1 2 | Set 2
| b c 9 a || 3 4 1 2 | 7 8 5 6 | Set 3
+---------++---------+---------+
| 4 1 2 3 || 8 5 6 7 | c 9 a b | Set 1
| 8 5 6 7 || c 9 a b | 4 1 2 3 | Set 2
| c 9 a b || 4 1 2 3 | 8 5 6 7 | Set 3
+---------++---------+---------+

David P Bird wrote:Each row must contain one of each number which means each number must be ommitted once only.
We can therefore compose an 8th row containing the ommitted numbers out of the 8 valid ones for each column.
Now try a methodical method of diagonally placing each number in the other 7 columns where it must appear.

Thank you for your reply. How do I determine which numbers must be omitted per column? I've made it down to the last row and it doesn't seem to work. Is this puzzle impossible to solve?

HelpPlease wrote:Thank you for your reply. How do I determine which numbers must be omitted per column? I've made it down to the last row and it doesn't seem to work. Is this puzzle impossible to solve?

OK, I’m trying to give you a lead on how to tackle this problem rather than spoiling it for you.
There are multiple solutions possible but it’s easiest to look for a very ordered one.

Add in that ‘missing’ 8th row so that every digit must be used once in each row with the rules for the sets staying the same.
Take each digit in turn and place it in a diagonal set of cells in the sets where it’s allowed to ensure it occurs 8 times.
Do this in an orderly way and you should be able to fill every cell.

Each time you find a solution it can be scrambled by swapping the rows, and the columns and digits in their respective sets.
This will give hundreds of possible solutions but which will all be essentially the same.