Perhaps check it again Posted March 12, 2015 Report Share Posted March 12, 2015 <------- 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? Quote Link to comment Share on other sites More sharing options...
0 gavinksong Posted March 13, 2015 Report Share Posted March 13, 2015 6 choose 3 = 20 1 Quote Link to comment Share on other sites More sharing options...
0 Perhaps check it again Posted March 14, 2015 Author Report Share Posted March 14, 2015 (edited) 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 March 14, 2015 by Perhaps check it again Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 14, 2015 Report Share Posted March 14, 2015 6 choose 3 = 20 Agree. Six moves, exactly three of which are to the right. 1 Quote Link to comment Share on other sites More sharing options...
0 Perhaps check it again Posted March 15, 2015 Author Report Share Posted March 15, 2015 (edited) 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 March 15, 2015 by Perhaps check it again Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 15, 2015 Report Share Posted March 15, 2015 AbABAbA ABAbABA 1 Quote Link to comment Share on other sites More sharing options...
Question
Perhaps check it again
<------- 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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