You need to make it so that all the numbers from 1 to 6 appear once in every row and column. You can only do that by "pushing" the rows down and the columns left. Each time you "push" a row or a column all the numbers in it move 1 block to the direction you have pushed it.

Can you complete the grid?

This is an interesting problem and takes a while to complete, but it is a great change from a traditional grid use logic problem

I don't care to write up exactly how to solve it, as I didn't write down what I figured out how and when, but the basic strategy I used was to keep track of what rows must be pushed before what columns, and what columns must be pushed before what rows.

For example, take a look at the column starting with 1. It contains a 3, but the bottom left corner also contains a 3. So that 3 must stay in the same column, which means the row below it is pushed, then that column, and then the row it's in.

Another key to this is to note that a number can only be pushed one square to the left on each row, and down on each column. Look at that 1 in the same column (the top square). If that were pushed before the top row, it would occupy the top left square. If it were pushed after, it would be in the square to the left of that.

This means that both ones in the top row (the one that starts with 1) need to be pushed down eventually, but more importantly, the top row needs to be pushed before the rightmost column.

Once you use that logic enough, you can end up with rows or columns in the final result with 4 or 5 numbers in them, and deduce what the remaining numbers are, and thus what rows need to be pushed before what columns in order for that number to land there.

There are fewer possibilities for the border squares, so I started on the left side and then worked on the bottom, top and right side before being able to have enough information about what was pushed when to find the whole solution by pushing those rows and columns in that order.

After finding the solution, I found it was the same as Charlie's, and also that rows and columns alternated, though it would be possible if the solution weren't unique that two rows or two columns would get pushed in a row.

Posted by Gamer on 2007-02-12 16:23:18