Edit i see a solution here i modify my question using suggestions and that solution.
Marble rolling toy solution.
Enjoy the course of rolling balls by combining blocks of various colors kumikumi slope of japanese company kumon.
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A marble is dropped at aa or bb.
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There are three levers in this figure let s say x1 x2 and x3 from left to right.
Model this toy by a finite automaton.
Above figure represents a marble rolling toy.
Whenever a marble encounters a lever it causes the lever to reverse after the marble passes so the next marble will take the opposite branch.
In fig 2 8 is a marble rolling toy.
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A marble is dropped at a or b.
Whenever a marble encounters a lever it causes the lever to reverse before the marble passes so the next marble will take the opposite branch.
There are three levers in this figure let s say x1 x2 and x3 from left to right.
A marble rolling toy in fig 2 8 is a marble rolling toy.
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Whenever a marble encounters a lever it causes the lever to reverse after the marble passes so the next marble will take the opposite.
A toy that rolls a ball.
For my question from this case i get the subcase.
According that solution exist a case.
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Mar 18 2019 explore dennie bomar s board marbles on pinterest.
Levers x 1 x 2 and x 3 cause the marble to fall either to the left or to the right.
And the ending is 1 and x mod 4 0 or x 3 mod 4 0 x is the numbers of 0 s and 1 s.
Above figure represents a marble rolling toy.
Whenever a marble encounters a lever it causes the lever to reverse after the marble passes so the next marble will take the opposite branch.
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A marble is dropped at a or b.
Levers x1 x2x1 x2 and x3x3 cause the marble to fall either to the left or to the right.