Solution to Challenge 2

Valley and mountain
- Valley fold: paper folds toward you, crease sinks. Mountain fold: paper folds away, crease points up.
- Turn the paper over and each crease swaps its name: the valley is now a mountain and the mountain is now a valley.

Script changes
- A3: w, h = 297, 420 gives square 297, strip 123 x 297, diagonal 420.0 (A-series sizes all share the ratio 1 : sqrt 2, so the trick works for every A size).
- Letter: w, h = 216, 279 gives square 216, strip 63 x 216, diagonal about 305.5 mm (rerun the script to confirm).
- The corner fold makes a square from ANY rectangle: the folded edge always gives a square whose side is the short edge. So Letter works too.
- What differs is the neat coincidence: for A sizes the square's diagonal equals the long side (297.0 vs 297), because the sides are in the ratio 1 : sqrt 2. For Letter the diagonal (about 305.5) is longer than the long side (279), because 279/216 is about 1.29, not 1.414. Answer: no, the diagonal is not the same as the long side for Letter.