Maximizing Points on a Grid: Strategies and Logic

In summary, the conversation was about a 5x5 grid that can be filled with numbers 1-4, with specific rules for placing them. The maximum sum for the grid was discussed, and a possible solution of 61 was given. The conversation also touched on the logic behind the placement of the numbers.
  • #1
martix
162
1
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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  • #2
How much did you get?
 
  • #3
59
But the question is - can it get better?
 
  • #4
martix said:
59
But the question is - can it get better?

Yes, I've got 61.
 
  • #5
Well, tell me how...
 
  • #6
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:
 

1. How do you determine the maximum number of points on a grid?

The maximum number of points on a grid is determined by the size of the grid and the rules of the game. For example, in a game of tic-tac-toe on a 3x3 grid, there can be a maximum of 9 points (each square is a point) but only 8 points can be occupied by players (since the center square is shared).

2. What strategies can be used to get the maximum points on a grid?

Some strategies that can be used to get the maximum number of points on a grid include analyzing the game rules, considering all possible moves, and anticipating your opponent's moves. It is also important to think ahead and plan your moves strategically.

3. Is it possible to get the maximum points on a grid every time?

It depends on the game and the skills of the players. In some games, such as Connect Four, it is possible to achieve the maximum number of points with the right strategy. However, in other games with more complex rules and variables, it may not be possible to get the maximum points every time.

4. How does the placement of points affect the maximum number of points on a grid?

The placement of points is crucial in determining the maximum number of points on a grid. In some games, certain positions may give players an advantage or disadvantage, affecting their ability to get the maximum points. It is important to consider all possible placements and their potential outcomes.

5. Can the maximum points on a grid be increased or decreased?

The maximum number of points on a grid is determined by the game rules and the size of the grid. It cannot be increased or decreased unless the rules are changed. However, the strategies used by players can impact the number of points they are able to achieve on the grid.

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