I have invented a new puzzle called Intersection. Let's find out what it is!

Intersection

You are given an $ntimes n$ grid with circles and boxes inside arbitrary squares. A circle cannot be in the same grid square as another box; there must always be at least two circles, but at least one box; the circles and/or boxes cannot fill up every square in the grid. Now onto the real rules of the game!

Suppose we let $n=3$ and have the following configuration:

$$begin{array}{|r|c|} hline
& & \ hline
&bigcirc &square \ hline
bigcirc & & \ hline
end{array}$$

The aim of the game in this case is to connect the two circles with lines, but the lines must intersect at the grid square with the box in the middle.

• Lines only start from circles, not boxes or anywhere else;


• When a line reaches an outer edge of the grid from a particular grid square, the line can be continued from the grid square on the directly opposite end of the same row/column, unless a line or circle is in the grid square on that very opposite end (kind of like how Pac-Man can leave the maze from one end and enter it back in from the directly opposite end);


• Lines cannot start from a circle and then connect back to the same circle;


• Lines cannot interfere with each other in regular grid squares, but only on the squares where the boxes are in;


• Lines can only travel in rows and columns, no diagonals;


• Up to four lines can protrude from a given circle in general, but that can vary depending on the position of a circle.


• Lines can only connect to other circles by crossing at least one grid square — if two circles are in grid squares adjacent to each other, a line cannot connect them in between.


• Lines must fill every grid square!

With those rules, here is the solution (though there could be more than one, but that I don't know for sure):

$qquadqquadqquadqquadqquadquad$

How about something else?

$$begin{array}{|r|c|} hline
& &bigcirc \ hline
&bigcirc & \ hline
square & & \ hline
end{array}$$

The solution to this is:

$qquadqquadqquadqquadqquadqquadquad$
(sorry for the bad drawing skill; trust me, I'm better by hand than by software, but that's besides the point)

So, let's bump it up to something a little harder, shall we?

Puzzle

Solve the following intersection grid!

$$begin{array}{|r|c|} hline
bigcirc& & & \ hline
& &bigcirc & \ hline
&square &square & \ hline
& &bigcirc &square \ hline
end{array}$$

The first user to answer with a solution will get the tick; another answer to follow that might also have a solution will get a $+50$ rep bounty; if an answer holds more than one solution, then it will get a $+100$ rep bounty (and if that one comes first, it will instead get the tick).

I hope my puzzle makes sense.

Good luck! :D

P.S. This game is like Flow for those who know that game, except the lines, well, intersect each other.

Edit: Turns out there is a game called Flow Free: Bridges such that lines can intersect each other. Unfortunately, this was unbeknownst to me when I created and posted this puzzle. My apologies.

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I think I've got an alternative solution to noedne

Here are two more solutions if we include the rule that at least two lines must protrude from a circle

It's not too different to the above, but I think this counts as

Another solution:

And here is one that is different

Another solution: