mathematics - Painting edges of a 3x3 grid with 4 colours

Can you paint the edges of a 3x3 grid with 4 colours, such that:

• The colours of edges of every 1x1 square are different.


• The colours of edges adjacent to every vertex are different.

Here is a similar puzzle for a 2x2 grid: Painting edges of a 2x2 grid with 4 colours

Good luck!

Answer

It would appear that

I can, as follows:

@ -1- @ -4- @ -1- @
|     |     |     |
2     3     2     3
|     |     |     |
@ -4- @ -1- @ -4- @
|     |     |     |

3     2     3     2
|     |     |     |
@ -1- @ -4- @ -1- @
|     |     |     |
2     3     2     3
|     |     |     |
@ -4- @ -1- @ -4- @

I further remark that

this pattern can be continued indefinitely, so it's no harder for (say) a 15x15 square.