Solution to Challenge 3

Method (Haga's first theorem)
1. Fold the square in half and unfold to mark the midpoint of the bottom edge.
2. Fold the top-left corner down to that midpoint and crease.
3. The folded-down top edge crosses the right edge at exactly 2/3 of the height from the bottom, so 1/3 from the top. Pinch to mark the point, then unfold.

Why it works (unit square)
- The fold sends the corner (0, 1) to (0.5, 0). The crease is the line y = 0.5x + 0.375.
- The top-right corner (1, 1) lands at (1.1, 0.8).
- The folded top edge runs from (0.5, 0) to (1.1, 0.8), with slope 4/3. At x = 1 it is at y = 0.667, which is 2/3.

Check with a ruler
- On a 15 cm square the mark is 10 cm from the bottom and 5 cm from the top.

Three equal strips
1. Fold the square flat along a horizontal crease through the mark (height 2/3).
2. Fold the bottom edge up onto that crease, which makes a second crease at height 1/3.
3. Unfold. The two creases divide the square into three strips of 5 cm each (on a 15 cm square).

Checkpoint: the mark is within about 1 mm of a third, and the three strips match.