Uniqueness of spanning tree on a grid. Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Graph - Minimum spanning treeCheapest spanning treeexistence of a spanning treeSpanning tree with unique paths.Euclidean Minimum Spanning Tree PropertyDirected spanning treeMinimum spanning tree for a weighted square gridGraph Theory(Spanning Tree)Spanning Tree Vs Minimum Spanning Treemaximum spanning tree
Is there such thing as an Availability Group failover trigger?
Does classifying an integer as a discrete log require it be part of a multiplicative group?
Can a new player join a group only when a new campaign starts?
Do square wave exist?
Is it common practice to audition new musicians 1-2-1 before rehearsing with the entire band?
How do I make this wiring inside cabinet safer? (Pic)
When a candle burns, why does the top of wick glow if bottom of flame is hottest?
Where are Serre’s lectures at Collège de France to be found?
Extracting terms with certain heads in a function
Do I really need recursive chmod to restrict access to a folder?
What would be the ideal power source for a cybernetic eye?
Has negative voting ever been officially implemented in elections, or seriously proposed, or even studied?
Is it ethical to give a final exam after the professor has quit before teaching the remaining chapters of the course?
Is safe to use va_start macro with this as parameter?
What is the meaning of the simile “quick as silk”?
Maximum summed powersets with non-adjacent items
What is the longest distance a player character can jump in one leap?
How to answer "Have you ever been terminated?"
What does the "x" in "x86" represent?
Is it fair for a professor to grade us on the possession of past papers?
Trademark violation for app?
How do I stop a creek from eroding my steep embankment?
Do wooden building fires get hotter than 600°C?
Compare a given version number in the form major.minor.build.patch and see if one is less than the other
Uniqueness of spanning tree on a grid.
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Graph - Minimum spanning treeCheapest spanning treeexistence of a spanning treeSpanning tree with unique paths.Euclidean Minimum Spanning Tree PropertyDirected spanning treeMinimum spanning tree for a weighted square gridGraph Theory(Spanning Tree)Spanning Tree Vs Minimum Spanning Treemaximum spanning tree
$begingroup$
When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!.
The game starts with a collection of "pipes" on a grid (centered on each vertex), clicking on a piece rotates it $90^circ$, and a piece can be rotated any number of times. The goal is to turn the final configuration of pipes into a spanning tree (of the grid graph), as shown in the screenshots below.
Example
Question
We left the conference with an unsolved question:
Are solutions to this puzzle always unique? Or is it possible to come up with a starting configuration (on any size grid) that has multiple trees as solutions?
(The prevailing guess is that solutions are unique, but nobody could manage to prove it.)
combinatorics graph-theory puzzle trees
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
$endgroup$
add a comment |
$begingroup$
When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!.
The game starts with a collection of "pipes" on a grid (centered on each vertex), clicking on a piece rotates it $90^circ$, and a piece can be rotated any number of times. The goal is to turn the final configuration of pipes into a spanning tree (of the grid graph), as shown in the screenshots below.
Example
Question
We left the conference with an unsolved question:
Are solutions to this puzzle always unique? Or is it possible to come up with a starting configuration (on any size grid) that has multiple trees as solutions?
(The prevailing guess is that solutions are unique, but nobody could manage to prove it.)
combinatorics graph-theory puzzle trees
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
$endgroup$
1
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago
add a comment |
$begingroup$
When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!.
The game starts with a collection of "pipes" on a grid (centered on each vertex), clicking on a piece rotates it $90^circ$, and a piece can be rotated any number of times. The goal is to turn the final configuration of pipes into a spanning tree (of the grid graph), as shown in the screenshots below.
Example
Question
We left the conference with an unsolved question:
Are solutions to this puzzle always unique? Or is it possible to come up with a starting configuration (on any size grid) that has multiple trees as solutions?
(The prevailing guess is that solutions are unique, but nobody could manage to prove it.)
combinatorics graph-theory puzzle trees
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
$endgroup$
When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!.
The game starts with a collection of "pipes" on a grid (centered on each vertex), clicking on a piece rotates it $90^circ$, and a piece can be rotated any number of times. The goal is to turn the final configuration of pipes into a spanning tree (of the grid graph), as shown in the screenshots below.
Example
Question
We left the conference with an unsolved question:
Are solutions to this puzzle always unique? Or is it possible to come up with a starting configuration (on any size grid) that has multiple trees as solutions?
(The prevailing guess is that solutions are unique, but nobody could manage to prove it.)
combinatorics graph-theory puzzle trees
combinatorics graph-theory puzzle trees
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
asked 5 hours ago
Peter KageyPeter Kagey
1,61772053
1,61772053
1
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago
add a comment |
1
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago
1
1
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No, solutions are not unique. The four "T" shaped pieces in the grid below can be rotated into either of two configurations:
┏━━━┓
┗┓╻╻┃
╺┫┣┛┃
┏┫┣╸┃
╹╹┗━┛
┏━━━┓
┗┓╻╻┃
╺┻┻┛┃
┏┳┳╸┃
╹╹┗━┛
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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%2fmath.stackexchange.com%2fquestions%2f3191645%2funiqueness-of-spanning-tree-on-a-grid%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
No, solutions are not unique. The four "T" shaped pieces in the grid below can be rotated into either of two configurations:
┏━━━┓
┗┓╻╻┃
╺┫┣┛┃
┏┫┣╸┃
╹╹┗━┛
┏━━━┓
┗┓╻╻┃
╺┻┻┛┃
┏┳┳╸┃
╹╹┗━┛
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
add a comment |
$begingroup$
No, solutions are not unique. The four "T" shaped pieces in the grid below can be rotated into either of two configurations:
┏━━━┓
┗┓╻╻┃
╺┫┣┛┃
┏┫┣╸┃
╹╹┗━┛
┏━━━┓
┗┓╻╻┃
╺┻┻┛┃
┏┳┳╸┃
╹╹┗━┛
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
add a comment |
$begingroup$
No, solutions are not unique. The four "T" shaped pieces in the grid below can be rotated into either of two configurations:
┏━━━┓
┗┓╻╻┃
╺┫┣┛┃
┏┫┣╸┃
╹╹┗━┛
┏━━━┓
┗┓╻╻┃
╺┻┻┛┃
┏┳┳╸┃
╹╹┗━┛
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
No, solutions are not unique. The four "T" shaped pieces in the grid below can be rotated into either of two configurations:
┏━━━┓
┗┓╻╻┃
╺┫┣┛┃
┏┫┣╸┃
╹╹┗━┛
┏━━━┓
┗┓╻╻┃
╺┻┻┛┃
┏┳┳╸┃
╹╹┗━┛
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 3 hours ago
edderioferedderiofer
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 3 hours ago
edderioferedderiofer
1561
answered 3 hours ago
edderioferedderiofer
1561
1561
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edderiofer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
add a comment |
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
Based on the picture in the question, all three ends of the T shapes have to connect to an adjacent piece; you can't have one end of the T run directly into the flat side of a | piece.
$endgroup$
– Misha Lavrov
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
It doesn't "run directly into the flat side of a | piece". There's actually a dead end "╸" piece in between, so this satisfies all the rules.
$endgroup$
– edderiofer
3 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
$begingroup$
Oh, I see. I couldn't quite read it in your answer, but it showed up when I highlighted it and now everything makes sense.
$endgroup$
– Misha Lavrov
2 hours ago
1
1
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
$begingroup$
Here is an interactive illustration of the solution: chiark.greenend.org.uk/~sgtatham/puzzles/js/…
$endgroup$
– Mike Earnest
2 hours ago
add a comment |
Thanks for contributing an answer to Mathematics 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%2fmath.stackexchange.com%2fquestions%2f3191645%2funiqueness-of-spanning-tree-on-a-grid%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
1
$begingroup$
This genre of logic puzzle is known originally as Netwalk.
$endgroup$
– Mike Earnest
4 hours ago
$begingroup$
@MikeEarnest, thanks for the reference. Based on this picture from this Reddit thread, it looks like (some versions of) Netwalk are on a torus instead of a grid—although that presents an interesting generalization of this question.
$endgroup$
– Peter Kagey
4 hours ago