Mfcttrf

Take elements from a list based on two criteria

Function argument returning void or non-void type

Is it possible to remotely hack the GPS system and disable GPS service worldwide?

Is it legal to meet with potential future employers in the UK, whilst visiting from the USA

Did this character show any indication of wanting to rule before S8E6?

Find this cartoon

Can a wizard copy a spell without first identifying it?

Why did Theresa May offer a vote on a second Brexit referendum?

On San Andreas Speedruns, why do players blow up the Picador in the mission Ryder?

Time complexity of an algorithm: Is it important to state the base of the logarithm?

Why did Jon Snow do this immoral act if he is so honorable?

USPS Back Room - Trespassing?

Is there any relationship between frequency of signal and distance it travels?

Can I tell a prospective employee that everyone in the team is leaving?

Why are Stein manifolds/spaces the analog of affine varieties/schemes in algebraic geometry?

How can I make an argument that my time is valuable?

Liars, truth-tellers and jokers

ESTA validity after a visa denial

What's difference between "depends on" and "is blocked by" relations between issues in Jira next-gen board?

How to keep consistency across the application architecture as a team grows?

How to deal with a colleague who is being aggressive?

便利な工具 what does な means

What did the 'turbo' button actually do?

Can a person survive on blood in place of water?

9x9 Map Path: In and out next to each other?

The robotic vacuum cleanerMosaic with tetris blocksStaking Out the IntegersHelp! I've forgotten my phone's lock pattern!Block the snake from reaching pointsThis ant sure is smart. But how fast is it?Squaring a crossPheno Menon and his coloured flagsCreate a map of a game's portalsLight Amplification by Stimulated Emission of Radiation

4

1

$begingroup$

This isn't something I read in a book or anything, it's more of a puzzle I thought up for myself.

However, I am unable to find a solution.

Here's my problem:

If I create a 9x9 checkerboard, and want to walk a path across it, where each block is walked upon only once, and there are only 90° turns, it's easy enough to create any path. (See first image example:)

However, if I want to create an entrance and exit point NEXT TO EACH OTHER, I am stumped. I can't do it:

Can someone help me think of a path ac cross a 9x9 area, where the entrance and exit points are directly next to each other, and yet each block is used only once and only 90° turns are used?

Thanks again.

pattern geometry

share|improve this question

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  From a glance I believe that it is impossible to do, but I have no proof other then just my intuition.
  $endgroup$
  – Rewan Demontay
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I also think that it is impossible to do. From the appearance of the problem I think that there will be an elegant mathematical proof
  $endgroup$
  – Adam
  3 hours ago
  

  
  
  
  

add a comment | 

4

1

$begingroup$

This isn't something I read in a book or anything, it's more of a puzzle I thought up for myself.

However, I am unable to find a solution.

Here's my problem:

If I create a 9x9 checkerboard, and want to walk a path across it, where each block is walked upon only once, and there are only 90° turns, it's easy enough to create any path. (See first image example:)

However, if I want to create an entrance and exit point NEXT TO EACH OTHER, I am stumped. I can't do it:

Can someone help me think of a path ac cross a 9x9 area, where the entrance and exit points are directly next to each other, and yet each block is used only once and only 90° turns are used?

Thanks again.

pattern geometry

share|improve this question

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  From a glance I believe that it is impossible to do, but I have no proof other then just my intuition.
  $endgroup$
  – Rewan Demontay
  3 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I also think that it is impossible to do. From the appearance of the problem I think that there will be an elegant mathematical proof
  $endgroup$
  – Adam
  3 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

This isn't something I read in a book or anything, it's more of a puzzle I thought up for myself.

However, I am unable to find a solution.

Here's my problem:

If I create a 9x9 checkerboard, and want to walk a path across it, where each block is walked upon only once, and there are only 90° turns, it's easy enough to create any path. (See first image example:)

However, if I want to create an entrance and exit point NEXT TO EACH OTHER, I am stumped. I can't do it:

Can someone help me think of a path ac cross a 9x9 area, where the entrance and exit points are directly next to each other, and yet each block is used only once and only 90° turns are used?

Thanks again.

pattern geometry

share|improve this question

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this question

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 3 hours ago

etsnymanetsnyman

1233

New contributor

etsnyman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 3 hours ago

etsnymanetsnyman

1233

1 Answer
1

active

oldest

votes

6

$begingroup$

It’s not possible.

Moving (stepping) only horizontally or vertically
(never moving diagonally or jumping over squares),
successive steps are always on squares of alternate colors. 
For example, in your first illustration, the first step is blue,
the second is pink, the third is blue again, and so on. 
In general, the odd-numbered steps are blue
and the even-numbered steps are pink.

Since both dimensions of your board are odd (9),
the total size is odd (9×9=81),
and so the last step, the 81st, is an odd number. 
Therefore, it must be the same color as the first square
(as seen in your first illustration). 
And, since adjacent (next-to-each-other) squares
are always different colors,
the exit square on an odd-sized board
cannot be next to the entrance square.

share|improve this answer

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. I guessed so, but I wasn't sure. Thanks for confirming it!
  $endgroup$
  – etsnyman
  2 hours ago
  

  
  
  
  

add a comment | 

Your Answer

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
);



);

etsnyman is a new contributor. Be nice, and check out our Code of Conduct.

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f84242%2f9x9-map-path-in-and-out-next-to-each-other%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

6

$begingroup$

It’s not possible.

Moving (stepping) only horizontally or vertically
(never moving diagonally or jumping over squares),
successive steps are always on squares of alternate colors. 
For example, in your first illustration, the first step is blue,
the second is pink, the third is blue again, and so on. 
In general, the odd-numbered steps are blue
and the even-numbered steps are pink.

Since both dimensions of your board are odd (9),
the total size is odd (9×9=81),
and so the last step, the 81st, is an odd number. 
Therefore, it must be the same color as the first square
(as seen in your first illustration). 
And, since adjacent (next-to-each-other) squares
are always different colors,
the exit square on an odd-sized board
cannot be next to the entrance square.

share|improve this answer

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. I guessed so, but I wasn't sure. Thanks for confirming it!
  $endgroup$
  – etsnyman
  2 hours ago
  

  
  
  
  

add a comment | 

6

$begingroup$

It’s not possible.

Moving (stepping) only horizontally or vertically
(never moving diagonally or jumping over squares),
successive steps are always on squares of alternate colors. 
For example, in your first illustration, the first step is blue,
the second is pink, the third is blue again, and so on. 
In general, the odd-numbered steps are blue
and the even-numbered steps are pink.

Since both dimensions of your board are odd (9),
the total size is odd (9×9=81),
and so the last step, the 81st, is an odd number. 
Therefore, it must be the same color as the first square
(as seen in your first illustration). 
And, since adjacent (next-to-each-other) squares
are always different colors,
the exit square on an odd-sized board
cannot be next to the entrance square.

share|improve this answer

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks. I guessed so, but I wasn't sure. Thanks for confirming it!
  $endgroup$
  – etsnyman
  2 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

It’s not possible.

Moving (stepping) only horizontally or vertically
(never moving diagonally or jumping over squares),
successive steps are always on squares of alternate colors. 
For example, in your first illustration, the first step is blue,
the second is pink, the third is blue again, and so on. 
In general, the odd-numbered steps are blue
and the even-numbered steps are pink.

Since both dimensions of your board are odd (9),
the total size is odd (9×9=81),
and so the last step, the 81st, is an odd number. 
Therefore, it must be the same color as the first square
(as seen in your first illustration). 
And, since adjacent (next-to-each-other) squares
are always different colors,
the exit square on an odd-sized board
cannot be next to the entrance square.

share|improve this answer

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

$endgroup$

share|improve this answer

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939

answered 3 hours ago

Peregrine RookPeregrine Rook

4,79821939