Maximizing Points on a Grid: Strategies and Logic

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Discussion Overview

The discussion revolves around maximizing the sum of numbers placed on a 5x5 grid, following specific placement rules for the numbers 1 through 4. Participants explore strategies for arrangement and the logic behind their approaches, focusing on both the theoretical and practical aspects of the problem.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant poses a challenge to find the maximum sum for a 5x5 grid filled with numbers 1 to 4, under specific neighbor rules.
  • Another participant claims to have achieved a sum of 59 and questions if it can be improved.
  • A different participant asserts they have reached a sum of 61, suggesting a possible improvement.
  • A subsequent post provides a specific arrangement of numbers that purportedly yields the sum of 61, inviting further discussion on the logic behind this configuration.

Areas of Agreement / Disagreement

Participants express differing results regarding the maximum sum achievable, with at least two competing sums (59 and 61) presented, indicating that the discussion remains unresolved regarding the optimal arrangement.

Contextual Notes

The discussion does not clarify the assumptions underlying the placement rules or the criteria for evaluating the sums, leaving potential gaps in understanding the problem's constraints.

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. :)
 
Last edited:
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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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