Series of wheel. Permutation

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Series of 77 wheel are connected. Let $k_i$ is $i$-wheel. My question is if $k_1$ moves $k_2$, $k_2$ moves $k_3$, $\dots$, $k_{77}$ moves $k_{1}$ then these system of wheels will be working?

My solution: Assume that $k_{77}$ is moved so $k_{76}$ is moved, $\dots$, $k_{2}$ is moved by $k_{1}$, which is moved by $k_{77}$. I think this is wrong. Can we explain what is wrong or give a hint?

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Hint: Let's say $k_1$ rotates clockwise.

  • Which way does $k_2$ rotate?
  • How about $k_3$?
  • How about $k_{77}$?
  • What does the above imply?