We need to join points so that they don't cross any other point


Total points = 9
Total connections possible = 9C2 = 36
Remove connections which passthrough a point:
There are 3 vertical lines, 3 horizontal lines and 2 main-diagonal lines, i.e. 8 lines

=> 36 - 8 = 28


Alternative approach (lets see which connections we are talking about):

Let the rows be named A B C and the columns 1 2 3 (like in chess )

Each point in the column 1 can be connected to a point in column 2 in 3 ways
Thus, there would be 3 x 3 = 9 connections ... (i)

Similarly, there would be 9 connections between points in column 2 and column 3 ... (ii)

We can do the exact same thing between row A and row B and again between row B and row C
However, we already have considered diagonal connections (ex. A1 to B2) above
So we need to only consider vertical connections (A1-B1, A2-B2 etc)

Thus, for rows A and B => 3 connections ... (iii)
For row B and row C => 3 connections ... (iv)

Now, we need to cosider connections from Row A to Row C along the extended diagonal
The only connections possible are A1-C2, A3-C2, A2-C1, A2-C3 => 4 connections ... (v)

The extended diagonal connections for the columns have already been considered in the 9 cases in (i) and the other 9 cases (ii)

Thus: 9 + 9 + 3 + 3 + 4 = 28
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