Question

A 6x6 grid is composed of 34 black squares and 2 white squares. All squares are randomly placed. In how many ways can the white squares be placed so that they have only one point in common?

a) 72
b) 144
c) 216
d) 288

Answer 1

The number of ways the white squares can be placed with only one point in common is 51.

Step-by-step explanation:

To find the number of ways the white squares can be placed so that they have only one point in common, we need to consider the placement of the first white square. There are 34 black squares, so the first white square can be placed in any of these 34 squares.

Once the first white square is placed, there are 33 black squares remaining. The second white square must be placed adjacent to the first white square, which means it must be placed in one of the 3 black squares adjacent to the first white square.

Therefore, the total number of ways the white squares can be placed is 34 * 3 = 102. However, we have counted each arrangement twice (once for each possible order of placing the white squares). So, the actual number of ways the white squares can be placed is 102 / 2 = 51.

Therefore, the correct answer is not provided in the options given.