Maximizing Points on a Grid: Strategies and Logic

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The discussion revolves around optimizing the placement of numbers 1 through 4 in a 5x5 grid while adhering to specific neighbor rules. The key rules state that 1 can be placed anywhere, 2 must be adjacent to 1, 3 must be adjacent to both 1 and 2, and 4 must be adjacent to 1, 2, and 3. The maximum sum achieved in the grid is initially reported as 59, but one participant claims to have reached a sum of 61. The optimal arrangement provided includes strategic placements of numbers to maximize the total while following the neighbor requirements. The conversation emphasizes the importance of logical reasoning in determining the best configuration for the grid.
martix
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Ok, I have a teaser and I want to check with all of you on what's 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. :)
 
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How much did you get?
 
59
But the question is - can it get better?
 
martix said:
59
But the question is - can it get better?

Yes, I've got 61.
 
Well, tell me how...
 
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

:smile:
 
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