# How to solve this 3x3 dots and lines puzzle?

I saw this on a forum and no one knows how to solve it, and it's driving me crazy. Does anyone know what the solution is and why? I tried looking at similarities in the columns, rows, and diagonals. I tried comparing everything to the top left or to the middle but that didn't help either. I tried seeing if there was a special pattern left in the gaps, but that wasn't helpful either.

Any clues?

It is the 3rd option on the top row from the left.

Reason

So in each row the formula is to overlay the first two shapes in the row (from left to right) and subtract the lines which overlap that are diagonal and subtract the lines which don't overlap if the lines are vertical or horizontal to produce the shape on the far right.

• You mean ...(from left to right)... not (from right to left) – John L Jan 21 at 18:11

I think the answer is

the third one from the left on the top row (which has three outer segments and nothing inside).

Reasoning:

For the three shapes on each row, think of a common operation that combines the first two to result in the third.

For the outer diamond part, the operation is XOR (include a segment if it appears in exactly one of the two input shapes):

/ \   /       \
+     =
\ /     /   \

\   / \   /
+     =
/           /

Therefore, the outer shape for the third row is

/ \         / \
+     =
/   \ /   \

For the inner part, the operation is to include only the segments that appear in both input shapes:

 |
- - +   - =   -
|     |     |

|
- - + -   = -
|

Therefore, the inner shape for the third row is

 |
-   +     = (nothing)
|

• Yeah basically what I said. – Smartest1here Jan 21 at 6:52