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Horizontally randomly moving particle


Perhaps check it again
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<------- g -------  f ------- e ------ d ------ c ------ b ------ A ------- B ------- C ------ D ------- E ------ F ------ G ------>

 

 

A particle originates at point A and can move left one point or move right point for any move.

It cannot be stationary for any move.

 

 

For two moves, the ways can be diagrammed like this:

 

ABC

ABA

Abc

AbA

 

 

Two of those ways begin and end with the particle at the starting point A.

 

 

Question:  For six moves, how many of the ways begin and end with the

particle at the starting point A?

 

 

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gavinksong,

 

your number of ways for the six moves versus mine is off by two.  I won't state

 

whether it's by lower or higher.  

 

I don't see your method as fitting here.  However, maybe it (your use of taking

 

combinations) can be used as part of a larger different method.

 

 

The problem is still open.

Edited by Perhaps check it again
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The ways that 6 moves that begin and end at point A can be diagrammed:

 

where the moves happen to be completely to the left of A

AbcdcbA

 

AbcbcbA

 

AbAbcbA

 

AbcbAbA

 

AbAbAbA

 

 

where the moves happen to be completely to the right of A

 

ABCDCBA

 

ABCBCBA

 

ABABCBA

 

ABCBABA

 

ABABABA

 

 

where the moves start to the left of A but then eventually cross A before ending at A

AbcbABA

 

AbAbABA

 

AbABCBA

 

AbABABA

 

 

where the moves start to the right of A but then eventually cross A before ending at A

 

ABCBAbA

 

ABABAbA

 

ABAbcbA

 

ABAbAbA

 

 

Does anyone see more ways (paths) for any of the four categories above? 

I am not seeing any more than what I listed in the spoilers.

Edited by Perhaps check it again
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