Hello, chil2e!

Two distinct circles and a square lie in the plane.

What is the maximum number of points of intersection of 2 or more of these 3 figures? We can "talk" our way through most of it.

Let represent the square and two circles.

We can "see" that:

. . and intersect in at most 2 points.

. . and intersect in at most 2 points.

. . and intersect in at most 2 points.

The maximum number of intersections is: .

Bottom line: is such a figure possible? Code:

* * * * * *
* * * *
* o *
* * * *
* * * *
* * - - o - o - - * *
* | * * | *
| |
* | * * | *
* | o | *
* | * * | *
* o * * o *
| |
* - - - - - - - *

Yes!