If there are 12 trees, 8 meters apart. The dog decides to mark his territory...but he takes the long way. What is the maximum distance?

Question

mhchen · Answer

Can you draw a diagram for a better visualization of the 'long way'?

mowrey · Answer

Sure. Would you like for me to paste the entire problem? I couldn't do it when I initially asked the question.

mhchen · Answer

O_o it's an actual question.

Can you screenshot it.

zepdrix · Answer

So the dog wants to mark each tree?
And we want to know in which order he should visit the trees so that the distance traveled is maximized?


Hmm interesting question :) I have no idea right now.. but sounds pretty cool.

mowrey · Answer

attachment

mowrey · Answer

The result is supposed to be 568, although I can't find that answer for some reason.

zepdrix · Answer

568?
Then what is this 528?
Was that your own attempt?

mowrey · Answer

Yes, that was my initial attempt, but it is not correct.

zepdrix · Answer

12 to 1 = 88m

From that point, you're standing at tree 1,
so shouldn't next travel

1 to 11

mowrey · Answer

And that's 80m.

mowrey · Answer

Oh, I see. Then next would be 2-10, etc.?

zepdrix · Answer

The next would be 11 to 2, right?
You start at your last ending point.

zepdrix · Answer

It seems that we're just traveling 8 meters less each time we do this.
And we're moving 12 different times... err actually 11 times because we're starting at one of the tree locations.

mowrey · Answer

I see, I'm miscounting something and I come short.

zepdrix · Answer

88 + 80 + 72 + 64 + 56 +
48 + 40 + 32 + 24 + 16 +
  8

zepdrix · Answer

Hmm that's 528 :O

zepdrix · Answer

Hmm :d

mowrey · Answer

Yep, it's quite weird.

mowrey · Answer

That might actually be correct. I'll leave it like that. Thanks for your help. :)

zepdrix · Answer

I wonder if going some weird zig zag pattern ends up being a longer distance overall. Like going
12 to 6
6 to 11
11 to 5
5 to 10

something like that... hmm

seratul · Answer

Maybe you can consider that the dog didn't even mark the first tree. But ran all the way to the 12th one, and then back to the first. So thats already 176.
I don't really know, but this question is very interesting.

mowrey · Answer

Someone was trying to make me understand the possibility of three trees instead, which there are six possible paths: abc acb bac bca cab cba.

seratul · Answer

Try googling this question. Bet you can find some interesting answers.

mowrey · Answer

Haven't been able to, not in this context at least...