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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  • Try to imagine a working system of 3 wheels connected in a loop...
    – Mike Earnest
    Sep 10 at 20:24










  • @MikeEarnest How do you work so damn fast lol.
    – Rushabh Mehta
    Sep 10 at 20:27














up vote
1
down vote

favorite












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?










share|cite|improve this question





















  • Try to imagine a working system of 3 wheels connected in a loop...
    – Mike Earnest
    Sep 10 at 20:24










  • @MikeEarnest How do you work so damn fast lol.
    – Rushabh Mehta
    Sep 10 at 20:27












up vote
1
down vote

favorite









up vote
1
down vote

favorite











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?










share|cite|improve this question













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?







combinatorics






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asked Sep 10 at 20:18







user448609


















  • Try to imagine a working system of 3 wheels connected in a loop...
    – Mike Earnest
    Sep 10 at 20:24










  • @MikeEarnest How do you work so damn fast lol.
    – Rushabh Mehta
    Sep 10 at 20:27
















  • Try to imagine a working system of 3 wheels connected in a loop...
    – Mike Earnest
    Sep 10 at 20:24










  • @MikeEarnest How do you work so damn fast lol.
    – Rushabh Mehta
    Sep 10 at 20:27















Try to imagine a working system of 3 wheels connected in a loop...
– Mike Earnest
Sep 10 at 20:24




Try to imagine a working system of 3 wheels connected in a loop...
– Mike Earnest
Sep 10 at 20:24












@MikeEarnest How do you work so damn fast lol.
– Rushabh Mehta
Sep 10 at 20:27




@MikeEarnest How do you work so damn fast lol.
– Rushabh Mehta
Sep 10 at 20:27










1 Answer
1






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2
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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?





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  • Oh my god. It's easy. Thanks. I closed question.
    – user448609
    Sep 10 at 20:31










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










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?





share|cite|improve this answer




















  • Oh my god. It's easy. Thanks. I closed question.
    – user448609
    Sep 10 at 20:31














up vote
2
down vote



accepted










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?





share|cite|improve this answer




















  • Oh my god. It's easy. Thanks. I closed question.
    – user448609
    Sep 10 at 20:31












up vote
2
down vote



accepted







up vote
2
down vote



accepted






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?





share|cite|improve this answer












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?






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answered Sep 10 at 20:27









John

22.2k32347




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  • Oh my god. It's easy. Thanks. I closed question.
    – user448609
    Sep 10 at 20:31
















  • Oh my god. It's easy. Thanks. I closed question.
    – user448609
    Sep 10 at 20:31















Oh my god. It's easy. Thanks. I closed question.
– user448609
Sep 10 at 20:31




Oh my god. It's easy. Thanks. I closed question.
– user448609
Sep 10 at 20:31

















 

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