0
$\begingroup$

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!

$\endgroup$
4
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ That's a better answer than mine, I'd say! But it would be interesting to ask for the total number of different solutions on an $n\times n$ grid. $\endgroup$ – WhatsUp Oct 7 at 0:59
  • $\begingroup$ Great find Gareth! Indeed it seems you can just use this pattern for larger grids. $\endgroup$ – Dmitry Kamenetsky Oct 7 at 0:59
  • 1
    $\begingroup$ @DmitryKamenetsky: It also extends to three dimensions, where you colour the faces shared between the cubical cells using 6 colours, no cell has two faces of the same colour, and no two faces of the same colour share an edge. $\endgroup$ – Jaap Scherphuis Oct 7 at 3:45
2
$\begingroup$

enter image description here

Again got it on the first try...

$\endgroup$
  • $\begingroup$ Ah... this time a bit late ^_^ $\endgroup$ – WhatsUp Oct 7 at 0:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.