Answers for Puzzles #2
I'll let someone else find this one.
Here are some hints: there are actually 4 words, of which abstemious is one. Two of the remaining three are so histrionic that none should be expected to find or know them without a very thick dictionary (although I'd be pleased if someone submitted those too!). The one that you should find starts with an 'f'.
"Facetious" is the easy of the three aeiou words. God knows what the other two are.
It can be done with no less than 8 triangles. Oh right, a solution would probably require a drawing too. Convince yourself why all the triangles in this picture are acute. Then I'll leave it up to you (or Sean) to prove why 8 is the minimum (look at the corners of the square, then look at the intersections of lines. What can you say about the constraints on both?)
He can steal virtually all of it!
He grabs rope 2 in one hand and ties the end of it to his belt. He then grabs rope 1 and ties the end of it to his belt too. Now he climbs rope 2 to halfway (ie. 20 ft from ceiling). He can now pull rope 1 taught and tie rope 1 around his waist (say he uses a knot on a bight) such that there are between 25 and 30 ft of rope 1 between him and the ceiling. Now, he continues to climb rope 2 to the very top. Using the knife, he cuts rope 2 where it meets the ceiling. He then swings (but not too severly we hope) around 10 feet obve the ground under rope two.
Now he pulls up rope 1 (which is now hanging from his waist and mostly coiled on the floor) and unties the end of rope 2 from his belt (he's still got it attached around his waist though). He ties the ends of rope 1 and rope 2 together into a really BIG knot (a stopper knot) to form a ~100 foot rope attached at one end to the ceiling and at the other to his belt. He is attached to the rope on a bight, around 25-30 feet from the ceiling.
Now for the trick. He climbs to the top of rope 1 and ties a loop on a bight under tension (phew!). He unties the end of rope 2 from his belt and feeds rope 1 through the loop until the stopper knot (at the midpoint of the 100 foot rope) meets the rope (and we'll assume the loop is small enough that the stopper knot won't fit through). He takes firm hold of the rope that he just fed through the loop (rope 2), near the top on the other side of the loop from the stopper knot.
He now cuts rope 1 just under the loop on a bight and uses rope 2 (suspended by stopper knot in the loop) to climb all the way down. He pulls on rope 1 (which is attached to the other end of the stopper knot) to feed rope 1 back out of the loop. The rope lands on the floor (or on him) and he has in his hands all 50 feet of rope 2 and 50 (minus epsilon) feet of rope 1.
If that was too much text, here's my friend Robin Clarke's version in pictures (hopefully your resolution allows for pictures of this size):






