In three nested squares (each joining the midpoints of the one around it), the corners of all three squares are marked. How many line segments join two marked points along a drawn line?

Each side of the outer square holds 3 marked points (a midpoint is a corner of the tilted square): 12. Each side of the tilted square also holds 3 (its midpoint is a corner of the inner square): 12. The inner square's sides hold 2 each: 4. Total $12+12+4=28$.