Riddle: carrying a couch up the stairs

Two people carry a couch up a flight of stairs, one at each end, both holding it from below and pushing straight up. Who carries more of the weight?

Answer

The person below, but not for the reason most people give.

If the couch were a thin plank held at its two ends, the split would be 50/50 at any angle. Tilting it shortens both horizontal lever arms by the same factor, cos θ, so the torques still balance in the middle.

A real couch is thick. Its center of mass sits some height h above the line between the two pairs of hands. Tilt it by θ and the center of mass moves horizontally toward the lower end, by h sin θ. Taking torques about the lower hands, with L the distance between the hands and W the weight:

Person above: W × (1/2 − (h/L) tan θ)
Person below: W × (1/2 + (h/L) tan θ)

For a 2 m couch with its center of mass 40 cm above the hands, on stairs at 35°, the person below carries about 64% of the weight. The steeper the stairs and the bulkier the couch, the worse it gets for them.