*Changed*
There is a man standing with a bear behind him, and a cliff 13 steps in front of him. The bear and cliff remain in the same locations, designated as step 0 and 13 receptively. If the man is on step 0, he will be killed by the bear, and anyone who is on step 13 will fall off the cliff. What are 12 directions, in the form of moving forward or back one step, one could give to the man to where he will stay alive after the 12th direction?

A) If he has to follow every 2nd direction?
B) If he has to follow every 3nd direction?

Forward a step = 1
Back a step = -1

Question

*Changed* 
There is a man standing with a bear behind him, and a cliff 13 steps in front of him. The bear and cliff remain in the same locations, designated as step 0 and 13 receptively. If the man is on step 0, he will be killed by the bear, and anyone who is on step 13 will fall off the cliff. What are 12 directions, in the form of moving forward or back one step, one could give to the man to where he will stay alive after the 12th direction?

A) If he has to follow every 2nd direction?
B) If he has to follow every 3nd direction?

Forward a step = 1
Back a step = -1

anonymous · Answer

attachment

anonymous · Answer

@Loser66

loser66 · Answer

I don't understand the problem @SithsAndGiggles

anonymous · Answer

After the 12th direction, the man cannot be on space 0 or 13

anonymous · Answer

@SolomonZelman

anonymous · Answer

It sounds like you're asked to set up a sequence of positive and negative 1's to denote a move in the forward/backward direction. What's to stop the man from moving back and forth endlessly, supposing he starts at any step other than 0 or 13? And does he start at step 1?

anonymous · Answer

Which is why there is a problem with following every 2nd step, 3rd step, etc

If you follow every 2nd step/3rd step.  I believe the question wants another set of answers other than just -1 +1, -1, +1,

anonymous · Answer

*or 1, 1, -1, -1
etc

anonymous · Answer

I think part b is impossible if you start at spot 0, but I may be wrong.

anonymous · Answer

I didn't mean that back and forth was the only way to go. I was just wondering if there are any extra rules against doing so.

And yes, I understand the issue with such a sequence if you're only considering every second term.

As for every third term, suppose we have the following set of directions
$$\{1,-1,1,-1,1,-1,\cdots\}$$
The back and forth strategy still works, and will continue to work for any odd number $n$ if you only allow every other $n$-th step. Not for evens, though.

anonymous · Answer

Ok.  Although, that doesn't answer my question if you are taking every 2nd direction.

anonymous · Answer

You can always construct a variation of the back-and-forth to suit your needs.

Consider $\{1,1,-1,-1,1,1,-1,-1,\cdots\}$. Every second term gives you the same sequence, $\{1,-1,1,-1,\cdots\}$.