harey

@bmad: I do not think my answer was the best one - after all, the chances were 50-50 phaze answered much better, he explained WHY.

I like the Phil1882 idea of modulo and tried the following rule: It works for some examples for N=4 (with no counterexample so far). The next steps should be an exhaustive computer simulation and a strong therie. Someone is willing to continue?

The first part did not require much calculation . As usually, I made an arithmetic error. I tried with b=60, c=80 - plasmid is correct.

They can follow other than mirror paths to meet at the same point. If they meet, they meet at the diagonal. The probability (for each one) to get to a particular point on the diagonal is: Pascal's triangle/(2 power n). I hope someone finds a formula for the product.

If I posted this problem, I would ask to clarify: 1) why the lines H and I cannot be parallel; 2) crossing trajectories do not necessarily imply that the ships collide. BTW, the sea should be endless (so that H does not reach her destination before colliding).

You got the first part to 97% - I wanted to hear "section of a pipeline along the trajectory". The tank of the U.S. scenario corresponds quite well to the pipeline, just the section of a tank is not measured in 1/m2, so the second part of the problem is still open.

I agree. (I just wanted to be VERY clear.)

"Rectangular Parallelepiped"s are usually not used to transport fuel.

Though correct, a little wordy. Can you imagine a physical object fitting this definition?

In Europe, we measure the fuel consumption in litres per 100 km. It is quite convenient because I can easily figure out what a litre is (a little bit less than one and half standard wine bottle) and it is not hard to figure out a distance of 100 km. However, any teacher of physics would point out that volume should be measured in [m3] and distance in [m]. After simplification, I get that fuel consumption should be measured in [m2]. What does it represent? In the U.S., the consumption is measured in miles/gallon. Quite convenient, too, just that in the MKSA system, I get [1/m2]. How do you represent that?

Is there a solution w/o equations? I mean more simple?

Still unsolved... I tried to omit chunks that are contained in other chunks (i.e. TGTGA is there twice and is contained in TGTGACA). I hoped that with the reminder I would be able to build longer chunks. Still too many combinations. How is it done in praxis?

I know a better variant: 6 butts, you need 3 butts to make a cigarette.