June 3rd, 2002, 4:21 pm
I'll take a crack, although I'm not confident.(1) With any box, you can slice some of the edges and flatten it out. But with some boxes, you will have sides overlapping. For example, a square torus box would require overlapping sides. If this does not count as lying flat then the answer is "sometimes," otherwise "always". Since this can be a surface with all right angles, and you say that can always be folded flap, I assume the latter.(2) I'm probably missing something here like yachts never race in 15-knot winds or yacht handicaps are a criminal offense in Northern Connecticut. But here's my feeble attempt. When you say the finish order is reversed and reduced by 1/3, I assume you mean the slowest boat in 5 knot winds (the 80 minute Class B finisher) is the fastest in 10 knot winds, and finishes 1/3 faster than the fastest 5 knot time, or in 40 minutes. Knowing nothing about yacht racing, I'm going to assume that average boat speed is a linear function of wind speed so a boat that completes a course in 80 minutes at 5 knots and 40 minutes at 10 knots will finish in 26 minutes 40 seconds in 15 knot winds.The fastest class A boat in 15 knot winds will be the 75-minute finisher in 5 knots and 43 minutes 20 seconds in 10 knots. I did use a calculator for this and the next step, but I did the first boat above in my head. The projected finish time in 15 knot winds is 30 minutes, 28.125 seconds.Therefore, if the Class A boats start 3 minutes 48.125 seconds before the B boats, we expect a dead heat for first place.