How do you do four Column solving

Arrange the first row arbitrarily: 1 2 3 4.

Then there is only one option to begin the next row: 3.

The remaining row must be 4 1 2.

This leaves no options for beginning the third row (1 and 3 are in the same column, and 2 and 4 share the diagonal).

Arrange the first row arbitrarily: 1 2 3 4.

Then there is only one option to begin the next row: 3.

The remaining row must be 4 1 2.

This leaves no options for beginning the third row (1 and 3 are in the same column, and 2 and 4 share the diagonal).