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Alice and Bob playing Neighboring Sums Game

Puzzling Asked on May 19, 2021

Alice and Bob are playing the neighbouring game

which is originally single game to get the highest point at the end.

You start with an empty 4×4 grid. At each
turn you can choose an empty cell and place a value in it. The placed
value is given by the following rules:

  • If the chosen cell has no neighboring (horizontal or vertical) values then the placed value is 1.
  • Otherwise the placed value is the sum of all neighboring (horizontal or vertical) values.

But this time, Alice and Bob are trying to get the highest total point by summing the values they put on the board with the rules by the Neighbouring Game. Alice puts a value on the board then next turn Bob puts and the game goes on. Alice starts the game with putting 1 somewhere on this 4×4 grid table, then Bob continues.

Who is likely to win the game at the end?

One Answer

The answer is

How?

Generalization:

Because:

Correct answer by Bubbler on May 19, 2021

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