Alex wants to cover a 30 by 30 board perfectly with 450 1 by 2 dominos. He also wants to ensure that he can trace a path between any 2 dominos that connect through at most N dominos. What is the minimum possible value of N which would allow Alex to form such a configuration?

16 you r wrong

To determine the minimum possible value of N that allows Alex to form a configuration where he can trace a path between any two dominos through at most N dominos, we need to consider the arrangement of the dominos on the board.

The 30 by 30 board has an area of 900 square units. Each 1 by 2 domino covers 2 square units, so we have a total of (900 / 2) = 450 dominos.

Now, we need to visualize how the dominos can be arranged on the board. One way to cover the board perfectly is by placing the dominos horizontally and vertically, alternating between them. This arrangement creates a grid pattern, where each horizontal domino pairs with a vertical one, and vice versa.

By alternating the placement of the dominos, we can observe that each row of the board will have either all horizontal dominos or all vertical dominos. Similarly, each column will have the opposite orientation.

To trace a path between any two dominos, we need to consider the maximum number of dominos between them. The maximum number of dominos between two dominos that are vertically aligned is the height of the board minus 1 (30 - 1) since there are no dominos in between vertically aligned ones. Similarly, the maximum number of dominos between two horizontally aligned dominos is the width of the board minus 1 (30 - 1).

Therefore, the minimum possible value of N that allows Alex to form such a configuration is given by the smaller of the two values: min(30 - 1, 30 - 1) = min(29, 29) = 29.

Hence, the minimum possible value of N is 29, which means Alex can trace a path between any two dominos through at most 29 dominos.