Maximum Height of a Hotel with Strange Elevators
$begingroup$
I encountered this puzzle many years ago, and I think back on it often as it is unique and thought provoking. As far as I know nobody has proved the given solution as optimum, so it may still be improved upon. I will provide the link to the original problem at the end.
I did reduce the complexity of the problem so that I can be sure of the solution to my less-intense version. Here's my version:
A hotel developer is building a new hotel, but he doesn't like elevators very much - he gets very confused by all the buttons, so he decided all of his elevators will only have one button. Long story short, each elevator will only stop on two floors. Being a sensible man, he will build more than one elevator shaft - six of them to be precise. He will also be using new MagLev elevator transport system - that means no cables and that means more than one elevator can be housed in a single shaft, as long as they don't have intersecting domains (he doesn't want any collisions!). For example: in the first shaft an elevator can be built that goes from floor 1 to floor 4. Only those two floors are serviced by that elevator. However in the same shaft a second elevator can be housed that will go from floor 5 to floor 7, and only those two floors, etc. The developer wants to be able to get from any floor in his hotel to any other floor with no more than 3 elevator trips. So, again, as an example: a guest can take elevator in the first shaft from floor 1 to floor 4, then take an elevator in the second shaft from floor 4 to floor 5 and then take the elevator in the first shaft again from floor 5 to floor 7. That will be 3 trips and the end of his adventure. Of course all the floors in the hotel need to be serviced! The question is what is the maximum number of floors that this developer can build for this hotel with these conditions?
If my version is a little too easy for you, try the harder version:
Same conditions as before, except each elevator can now stop at 6 floors.
Here's the link to where I first saw this: Elevator Efficiency
mathematics computer-puzzle graph-theory
asked 13 mins ago
AmorydaiAmorydai
6169
$endgroup$
add a comment |
$begingroup$
I encountered this puzzle many years ago, and I think back on it often as it is unique and thought provoking. As far as I know nobody has proved the given solution as optimum, so it may still be improved upon. I will provide the link to the original problem at the end.
I did reduce the complexity of the problem so that I can be sure of the solution to my less-intense version. Here's my version:
A hotel developer is building a new hotel, but he doesn't like elevators very much - he gets very confused by all the buttons, so he decided all of his elevators will only have one button. Long story short, each elevator will only stop on two floors. Being a sensible man, he will build more than one elevator shaft - six of them to be precise. He will also be using new MagLev elevator transport system - that means no cables and that means more than one elevator can be housed in a single shaft, as long as they don't have intersecting domains (he doesn't want any collisions!). For example: in the first shaft an elevator can be built that goes from floor 1 to floor 4. Only those two floors are serviced by that elevator. However in the same shaft a second elevator can be housed that will go from floor 5 to floor 7, and only those two floors, etc. The developer wants to be able to get from any floor in his hotel to any other floor with no more than 3 elevator trips. So, again, as an example: a guest can take elevator in the first shaft from floor 1 to floor 4, then take an elevator in the second shaft from floor 4 to floor 5 and then take the elevator in the first shaft again from floor 5 to floor 7. That will be 3 trips and the end of his adventure. Of course all the floors in the hotel need to be serviced! The question is what is the maximum number of floors that this developer can build for this hotel with these conditions?
If my version is a little too easy for you, try the harder version:
Same conditions as before, except each elevator can now stop at 6 floors.
Here's the link to where I first saw this: Elevator Efficiency
mathematics computer-puzzle graph-theory
asked 13 mins ago
AmorydaiAmorydai
6169
$endgroup$
add a comment |
$begingroup$
I encountered this puzzle many years ago, and I think back on it often as it is unique and thought provoking. As far as I know nobody has proved the given solution as optimum, so it may still be improved upon. I will provide the link to the original problem at the end.
I did reduce the complexity of the problem so that I can be sure of the solution to my less-intense version. Here's my version:
A hotel developer is building a new hotel, but he doesn't like elevators very much - he gets very confused by all the buttons, so he decided all of his elevators will only have one button. Long story short, each elevator will only stop on two floors. Being a sensible man, he will build more than one elevator shaft - six of them to be precise. He will also be using new MagLev elevator transport system - that means no cables and that means more than one elevator can be housed in a single shaft, as long as they don't have intersecting domains (he doesn't want any collisions!). For example: in the first shaft an elevator can be built that goes from floor 1 to floor 4. Only those two floors are serviced by that elevator. However in the same shaft a second elevator can be housed that will go from floor 5 to floor 7, and only those two floors, etc. The developer wants to be able to get from any floor in his hotel to any other floor with no more than 3 elevator trips. So, again, as an example: a guest can take elevator in the first shaft from floor 1 to floor 4, then take an elevator in the second shaft from floor 4 to floor 5 and then take the elevator in the first shaft again from floor 5 to floor 7. That will be 3 trips and the end of his adventure. Of course all the floors in the hotel need to be serviced! The question is what is the maximum number of floors that this developer can build for this hotel with these conditions?
If my version is a little too easy for you, try the harder version:
Same conditions as before, except each elevator can now stop at 6 floors.
Here's the link to where I first saw this: Elevator Efficiency
mathematics computer-puzzle graph-theory
asked 13 mins ago
AmorydaiAmorydai
6169
$endgroup$
I encountered this puzzle many years ago, and I think back on it often as it is unique and thought provoking. As far as I know nobody has proved the given solution as optimum, so it may still be improved upon. I will provide the link to the original problem at the end.
I did reduce the complexity of the problem so that I can be sure of the solution to my less-intense version. Here's my version:
A hotel developer is building a new hotel, but he doesn't like elevators very much - he gets very confused by all the buttons, so he decided all of his elevators will only have one button. Long story short, each elevator will only stop on two floors. Being a sensible man, he will build more than one elevator shaft - six of them to be precise. He will also be using new MagLev elevator transport system - that means no cables and that means more than one elevator can be housed in a single shaft, as long as they don't have intersecting domains (he doesn't want any collisions!). For example: in the first shaft an elevator can be built that goes from floor 1 to floor 4. Only those two floors are serviced by that elevator. However in the same shaft a second elevator can be housed that will go from floor 5 to floor 7, and only those two floors, etc. The developer wants to be able to get from any floor in his hotel to any other floor with no more than 3 elevator trips. So, again, as an example: a guest can take elevator in the first shaft from floor 1 to floor 4, then take an elevator in the second shaft from floor 4 to floor 5 and then take the elevator in the first shaft again from floor 5 to floor 7. That will be 3 trips and the end of his adventure. Of course all the floors in the hotel need to be serviced! The question is what is the maximum number of floors that this developer can build for this hotel with these conditions?
If my version is a little too easy for you, try the harder version:
Same conditions as before, except each elevator can now stop at 6 floors.
Here's the link to where I first saw this: Elevator Efficiency
mathematics computer-puzzle graph-theory
mathematics computer-puzzle graph-theory
asked 13 mins ago
AmorydaiAmorydai
6169
asked 13 mins ago
AmorydaiAmorydai
6169
asked 13 mins ago
AmorydaiAmorydai
6169
asked 13 mins ago
AmorydaiAmorydai
6169
asked 13 mins ago
AmorydaiAmorydai
6169
6169
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "559"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f80173%2fmaximum-height-of-a-hotel-with-strange-elevators%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Puzzling Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f80173%2fmaximum-height-of-a-hotel-with-strange-elevators%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
