$n$ buttons on a table
$begingroup$
A generalization of Four buttons on a table:
In a certain room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either ”on” or ”off”, however one cannot
tell its the current state by its appearance. The room is lighted if and only if all the buttons are all ”on”, and there is nobody inside.
• A person is (repeatedly) allowed to enter the room, and press whichever buttons
she likes. After she steps out, she is told whether she succeeded to put the light
on. At the same time, a table rotates in an unknown manner.
The goal is:
to design a deterministic strategy to put the light on, no matter what is the initial state of the buttons.
As a bonus I was given:
The same above but with: $$n = 2^k$$ symmetrically (with respect to rotation) located buttons.
Assuming that the problem is always solvable for $n=2^k$ buttons, for which configurations of button states is it solvable when $n$ is any positive integer?
logical-deduction strategy
asked 7 mins ago
noednenoedne
6,49011956
$endgroup$
add a comment |
$begingroup$
A generalization of Four buttons on a table:
In a certain room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either ”on” or ”off”, however one cannot
tell its the current state by its appearance. The room is lighted if and only if all the buttons are all ”on”, and there is nobody inside.
• A person is (repeatedly) allowed to enter the room, and press whichever buttons
she likes. After she steps out, she is told whether she succeeded to put the light
on. At the same time, a table rotates in an unknown manner.
The goal is:
to design a deterministic strategy to put the light on, no matter what is the initial state of the buttons.
As a bonus I was given:
The same above but with: $$n = 2^k$$ symmetrically (with respect to rotation) located buttons.
Assuming that the problem is always solvable for $n=2^k$ buttons, for which configurations of button states is it solvable when $n$ is any positive integer?
logical-deduction strategy
asked 7 mins ago
noednenoedne
6,49011956
$endgroup$
add a comment |
$begingroup$
A generalization of Four buttons on a table:
In a certain room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either ”on” or ”off”, however one cannot
tell its the current state by its appearance. The room is lighted if and only if all the buttons are all ”on”, and there is nobody inside.
• A person is (repeatedly) allowed to enter the room, and press whichever buttons
she likes. After she steps out, she is told whether she succeeded to put the light
on. At the same time, a table rotates in an unknown manner.
The goal is:
to design a deterministic strategy to put the light on, no matter what is the initial state of the buttons.
As a bonus I was given:
The same above but with: $$n = 2^k$$ symmetrically (with respect to rotation) located buttons.
Assuming that the problem is always solvable for $n=2^k$ buttons, for which configurations of button states is it solvable when $n$ is any positive integer?
logical-deduction strategy
asked 7 mins ago
noednenoedne
6,49011956
$endgroup$
A generalization of Four buttons on a table:
In a certain room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either ”on” or ”off”, however one cannot
tell its the current state by its appearance. The room is lighted if and only if all the buttons are all ”on”, and there is nobody inside.
• A person is (repeatedly) allowed to enter the room, and press whichever buttons
she likes. After she steps out, she is told whether she succeeded to put the light
on. At the same time, a table rotates in an unknown manner.
The goal is:
to design a deterministic strategy to put the light on, no matter what is the initial state of the buttons.
As a bonus I was given:
The same above but with: $$n = 2^k$$ symmetrically (with respect to rotation) located buttons.
Assuming that the problem is always solvable for $n=2^k$ buttons, for which configurations of button states is it solvable when $n$ is any positive integer?
logical-deduction strategy
logical-deduction strategy
asked 7 mins ago
noednenoedne
6,49011956
asked 7 mins ago
noednenoedne
6,49011956
asked 7 mins ago
noednenoedne
6,49011956
asked 7 mins ago
noednenoedne
6,49011956
asked 7 mins ago
noednenoedne
6,49011956
6,49011956
add a comment |
add a comment |
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