Solution for #8

Alternate Solution #1

Almost all of it. First tie the ropes together at the ends. then climb one of the ropes. Tie a loop in the rope as close to the ceiling as possible. Hang from the loop, then cut the rope just below it (but don't drop it, or you'll be stuck on the ceiling). Run the rope through the loop and tie it to your waist. Swing over to the other rope and pull the rope that's going through the loop tight. Cut the other rope as close as possible to the ceiling, holding tight to the end of it. Once the rope is loose, you will swing down below the loop. Let yourself down to the ground by letting the rope out. At the bottom, untie yourself and pull the rope completely through the loop. At this point you'll have all of the rope except what was used to tie the loop.

Alternate Solution #2

All the rope, provided that the knife is such that: it can support your weight when half the blade is stuck in ceiling, and it can bend at the blade-handle junction without breaking. Climb to top of the first rope, bringing other rope along. At the top, stretch the second rope toward you and circle it around your waist. Cut the first rope at the ceilling, hang on, and swing down on the second rope. Climb back up to the ceiling. Pull up the other end of the second rope, and tie it to the end of the first rope. Loop the tied ropes around the handle of the knife. In one (quick) motion, cut the second rope at the ceiling while pushing the knife into the ceiling. Bend the handle of the knife enough so that the rope won't slip out. Go down, hanging on the double rope with both hands. At the floor, jerk hard to release the knife and the rest of the rope.

Alternate Solution #3

Climb up the first rope, carrying up the end of the second with you. Cut the first rope, flush with the ceiling, swinging down on the second. Climb up the second and cut that flush with the ceiling too, but only part way, until it can just barely hold the rest of your weight. Slowly climb down until you're just short of the bottom. Tie a small loop here and climb up about two feet. Secure the loop about your feet and fall to the ground (roughly three feet). Just before your feet hit the ground the force of the fall will snap the rope at the top.