Getting max points on a grid

martix

Ok, I have a teaser and I want to check with all of you on whats the most points.
We have a 5x5 grid. That grid can be filled with numbers 1 thru 4. There are rules to placing these. Diagonal directions do not count as neighbours. 1 can be placed anywhere; 2 needs to have 1 as a neighbour; 3 needs 1 and 2; and 4 needs to have 1, 2 and 3 as neighbours. Whats the maximum sum for the whole grid and how should the numbers be placed.

P.S. Also - throw out those wacky number and whatever else theories and tell me why and how - the logic behind these. :)

Rogerio

How much did you get?

martix

59
But the question is - can it get better?

Rogerio

Yes, I've got 61.

martix

Well, tell me how...

Rogerio

OK...

1 3 2 1 2
2 4 4 1 4
3 1 3 2 3
4 2 4 4 1
1 3 1 3 2