Yeah Steve,
bplus Conjecture: this train puzzle and the Towers of Hanoi puzzle solutions have a one to one map, so that any amount of cars or disks can be shuffled by same set of ordered steps.
Too bad I am not enough of a mathematician to show this formally, BUT it'd probably go over everyones head and patience tolerance to follow anyway, including my own!
PS, the only difference that I can see is for the train puzzle, one of the pegs is shorter than the other 2 so that any amount of cars or pegs can not be parked on it at one time.
OH! That would be a nice variation on that Towers puzzle!
bplus Conjecture: this train puzzle and the Towers of Hanoi puzzle solutions have a one to one map, so that any amount of cars or disks can be shuffled by same set of ordered steps.
Too bad I am not enough of a mathematician to show this formally, BUT it'd probably go over everyones head and patience tolerance to follow anyway, including my own!
PS, the only difference that I can see is for the train puzzle, one of the pegs is shorter than the other 2 so that any amount of cars or pegs can not be parked on it at one time.
OH! That would be a nice variation on that Towers puzzle!
b = b + ...