Mixing
Garage Door Puzzle
Clash Royale CLAN TAG#URR8PPP
up vote
6
down vote
favorite
When I drive home, I open my garage door from my truck. I cannot see the garage door until I turn into my driveway. I want to know the range of my opener. How close can I get to knowing the farthest distance at which it will open in one drive down the road towards my house?
Assumptions for simplicity:
The door takes exactly 10 seconds to open or close fully. (And it closes at a uniform rate).
The road leading past the house is straight.
The distance from the road to the garage is negligibile.
I can click the opener as many times as I want.
If I click the opener while the door is closing, it begins opening and vice versa.
I can discern differences in the height of the door as small as 6 inches, meaning I can tell the difference between 1/2 and 1/3rd, but not between 1/5th and 1/6th. (These numbers are largely arbitrary - basically, I want a practical solution that doesn't involve measuring the final height of the door with lasers and levels)
Finally, I know how far away I am at any time. I know the opener doesn't work at 150 feet and does work at 50 feet. [Edit credit: joriki]
This is my first time posting here, so please let me know if there are any additional details I ought to add. Thanks!
geometry puzzle
asked Jul 25 at 16:40
Zara
336
 |Â
show 3 more comments
up vote
6
down vote
favorite
When I drive home, I open my garage door from my truck. I cannot see the garage door until I turn into my driveway. I want to know the range of my opener. How close can I get to knowing the farthest distance at which it will open in one drive down the road towards my house?
Assumptions for simplicity:
The door takes exactly 10 seconds to open or close fully. (And it closes at a uniform rate).
The road leading past the house is straight.
The distance from the road to the garage is negligibile.
I can click the opener as many times as I want.
If I click the opener while the door is closing, it begins opening and vice versa.
I can discern differences in the height of the door as small as 6 inches, meaning I can tell the difference between 1/2 and 1/3rd, but not between 1/5th and 1/6th. (These numbers are largely arbitrary - basically, I want a practical solution that doesn't involve measuring the final height of the door with lasers and levels)
Finally, I know how far away I am at any time. I know the opener doesn't work at 150 feet and does work at 50 feet. [Edit credit: joriki]
This is my first time posting here, so please let me know if there are any additional details I ought to add. Thanks!
geometry puzzle
asked Jul 25 at 16:40
Zara
336
1
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06
 |Â
show 3 more comments
up vote
6
down vote
favorite
up vote
6
down vote
favorite
When I drive home, I open my garage door from my truck. I cannot see the garage door until I turn into my driveway. I want to know the range of my opener. How close can I get to knowing the farthest distance at which it will open in one drive down the road towards my house?
Assumptions for simplicity:
The door takes exactly 10 seconds to open or close fully. (And it closes at a uniform rate).
The road leading past the house is straight.
The distance from the road to the garage is negligibile.
I can click the opener as many times as I want.
If I click the opener while the door is closing, it begins opening and vice versa.
I can discern differences in the height of the door as small as 6 inches, meaning I can tell the difference between 1/2 and 1/3rd, but not between 1/5th and 1/6th. (These numbers are largely arbitrary - basically, I want a practical solution that doesn't involve measuring the final height of the door with lasers and levels)
Finally, I know how far away I am at any time. I know the opener doesn't work at 150 feet and does work at 50 feet. [Edit credit: joriki]
This is my first time posting here, so please let me know if there are any additional details I ought to add. Thanks!
geometry puzzle
asked Jul 25 at 16:40
Zara
336
When I drive home, I open my garage door from my truck. I cannot see the garage door until I turn into my driveway. I want to know the range of my opener. How close can I get to knowing the farthest distance at which it will open in one drive down the road towards my house?
Assumptions for simplicity:
The door takes exactly 10 seconds to open or close fully. (And it closes at a uniform rate).
The road leading past the house is straight.
The distance from the road to the garage is negligibile.
I can click the opener as many times as I want.
If I click the opener while the door is closing, it begins opening and vice versa.
I can discern differences in the height of the door as small as 6 inches, meaning I can tell the difference between 1/2 and 1/3rd, but not between 1/5th and 1/6th. (These numbers are largely arbitrary - basically, I want a practical solution that doesn't involve measuring the final height of the door with lasers and levels)
Finally, I know how far away I am at any time. I know the opener doesn't work at 150 feet and does work at 50 feet. [Edit credit: joriki]
This is my first time posting here, so please let me know if there are any additional details I ought to add. Thanks!
geometry puzzle
asked Jul 25 at 16:40
Zara
336
edited Jul 25 at 16:58
asked Jul 25 at 16:40
Zara
336
asked Jul 25 at 16:40
Zara
336
asked Jul 25 at 16:40
Zara
336
336
1
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06
 |Â
show 3 more comments
1
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06
1
1
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06
 |Â
show 3 more comments
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
You could drive at such a speed that you cover the first 10 feet in 5 seconds, the second 10 feet in 2.5 seconds, the third 10 feet in 1.25 seconds, etc. At each 10 foot mark press the remote. When you get to the garage, the height of the door will tell you when the remote first worked. You'll have your answer to withing 5 feet.
(This may require lasers, after all. And you might burn up in the atmosphere just as you arrive. But this is math, so practical considerations no matter.)
answered Jul 25 at 17:13
B. Goddard
16.4k21238
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
You could drive at such a speed that you cover the first 10 feet in 5 seconds, the second 10 feet in 2.5 seconds, the third 10 feet in 1.25 seconds, etc. At each 10 foot mark press the remote. When you get to the garage, the height of the door will tell you when the remote first worked. You'll have your answer to withing 5 feet.
(This may require lasers, after all. And you might burn up in the atmosphere just as you arrive. But this is math, so practical considerations no matter.)
answered Jul 25 at 17:13
B. Goddard
16.4k21238
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
add a comment |Â
up vote
1
down vote
accepted
You could drive at such a speed that you cover the first 10 feet in 5 seconds, the second 10 feet in 2.5 seconds, the third 10 feet in 1.25 seconds, etc. At each 10 foot mark press the remote. When you get to the garage, the height of the door will tell you when the remote first worked. You'll have your answer to withing 5 feet.
(This may require lasers, after all. And you might burn up in the atmosphere just as you arrive. But this is math, so practical considerations no matter.)
answered Jul 25 at 17:13
B. Goddard
16.4k21238
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
You could drive at such a speed that you cover the first 10 feet in 5 seconds, the second 10 feet in 2.5 seconds, the third 10 feet in 1.25 seconds, etc. At each 10 foot mark press the remote. When you get to the garage, the height of the door will tell you when the remote first worked. You'll have your answer to withing 5 feet.
(This may require lasers, after all. And you might burn up in the atmosphere just as you arrive. But this is math, so practical considerations no matter.)
answered Jul 25 at 17:13
B. Goddard
16.4k21238
You could drive at such a speed that you cover the first 10 feet in 5 seconds, the second 10 feet in 2.5 seconds, the third 10 feet in 1.25 seconds, etc. At each 10 foot mark press the remote. When you get to the garage, the height of the door will tell you when the remote first worked. You'll have your answer to withing 5 feet.
(This may require lasers, after all. And you might burn up in the atmosphere just as you arrive. But this is math, so practical considerations no matter.)
answered Jul 25 at 17:13
B. Goddard
16.4k21238
answered Jul 25 at 17:13
B. Goddard
16.4k21238
answered Jul 25 at 17:13
B. Goddard
16.4k21238
answered Jul 25 at 17:13
B. Goddard
16.4k21238
16.4k21238
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
add a comment |Â
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Ha! This actually made me laugh. Quite a nice solution (though I think the first 10 feet could take 10 seconds). Thanks for writing!
– Zara
Jul 26 at 17:18
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
Yeah. I also thought there might be a Fibonacci search that would allow you to keep your speed a bit lower than this binary one.... but I gave up.
– B. Goddard
Jul 26 at 19:58
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2862596%2fgarage-door-puzzle%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
1
I think you need a prior on the distance. The solution will be some form of pattern of distances at which you click the opener so as to be able to infer the first one that worked from the resulting heights; but exactly how to place those distances will depend on your prior for the distance. E.g., if you believe that it's something around $200textm$, you'd concentrate your clicks near that distance.
– joriki
Jul 25 at 16:50
If this is a real problem and not just a nice abstraction then solve it with two people, one watching the garage door and the other walking away down the block clicking to open and close. Shout back and forth, or text back and forth, or manage the experiment with an agreed upon schedule with synchronized watches.
– Ethan Bolker
Jul 25 at 17:03
@joriki - thanks for the suggestions. I have incorporated the change above
– Zara
Jul 25 at 17:04
I would just do it with binary search, ignoring the timing information. Go 100 feet away and test. If it opens at 100, go 125, otherwise go 75. Keep splitting the range in half until you are as close as you want.
– Ross Millikan
Jul 25 at 17:05
@EthanBolker - it is a simplified version of my actual setup and I've been puzzling over how to do it myself, but now I'm curious about the math of it as well.
– Zara
Jul 25 at 17:06