Series of wheel. Permutation
Clash Royale CLAN TAG#URR8PPP
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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?
combinatorics
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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?
combinatorics
Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27
add a comment |Â
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?
combinatorics
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
combinatorics
asked Sep 10 at 20:18
user448609
Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27
add a comment |Â
Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27
Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27
add a comment |Â
1 Answer
1
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?
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
add a comment |Â
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?
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
add a comment |Â
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?
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
add a comment |Â
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?
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?
answered Sep 10 at 20:27
John
22.2k32347
22.2k32347
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
add a comment |Â
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
Oh my god. It's easy. Thanks. I closed question.
â user448609
Sep 10 at 20:31
add a comment |Â
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Try to imagine a working system of 3 wheels connected in a loop...
â Mike Earnest
Sep 10 at 20:24
@MikeEarnest How do you work so damn fast lol.
â Rushabh Mehta
Sep 10 at 20:27