Quote Originally Posted by Xei View Post
Sorry tommo, didn't see the posts. To be fair you did put them in a silly place.
Hehe. Probably didn't understand my post in the meta forum thread then about time-travel.

Quote Originally Posted by Xei View Post
If it were the highest number on the die that determined the winner then A would indeed always beat C. But as I imagine you guessed, it's not true. It seems very obvious, but if you relied on this intuition, and a reason that you 'know but can't put into words', you'd be incorrect. It is of course normally true. But there are various dice for which it is not true. For instance,

die A has sides: 2, 2, 4, 4, 9, 9
die B has sides: 1, 1, 6, 6, 8, 8
die C has sides: 3, 3, 5, 5, 7, 7.

You can work out the probabilities of A beating B and so on (any pair of numbers from the two dice is equally likely to come up, so just count the ones which win). You find that the probability that A rolls a higher number than B is 5/9 (55.55%), the probability that B rolls a higher number than C is 5/9, and the probability that C rolls a higher number than A is 5/9.
So.... yes my "intuition" or whatever, was correct.
(Not really intuition, I did think about it a bit, just not too much).

Quote Originally Posted by Xei View Post
Like all of these things, the answer is hard to get, but very easy to understand. It can be explained in two or three short sentences, I think.
Ok what about this....
There will be, at worst (because any more of each will create multiple circuits of one transport type), 7 buses and 8 trains.

Ala,


The one from top left to bottom right can be red, otherwise it creates 2 green circuits. But making it red creates a red circuit.



And breaking that circuit in any way will create a green circuit (light green and yellow are green ones breaking red circuit).



This I guess is still not proof, but you can't prove it wrong at least. So fuck it.

Quote Originally Posted by PhilosopherStoned View Post
Since people are playing again, I'll hold off on solutions. I will give a counter-example to the claim that one can circum-navigate the mountain by starting at the stop with the most fuel...

We'll have four depots. One has one third of the gas and each of the other three has two ninths. Starting from the stop with one third, one can traverse the circle in either direction and can hence potentially reach any point on two thirds of the circle. So one only needs to cluster the remaining three depots within the remaining one third of the circle to assure that starting at the point with the most gas will end in failure.
And fuck you.