Transferring 9 pegs on a 9x9 gridProfessor Halfbrain and the 9x9 chessboard (Part 2)A Puzzling GridReassembling the Marquetry II: The Coffee Table Strikes BackDoes this mathy square have any solutions? (And how many?)Place 4x12 detainees on a 7x7 grid of cellsIntroducing: Sudoku-JanpuThe very special matrixSolving a Rullo PuzzlePainting a 4x6 grid with 2 coloursPaint 10 cells of a 10x10 grid
What are the consequences for downstream actors of redistributing a work under a wider CC license than the copyright holder authorized?
What causes standard door hinges to close up to a certain amount automatically?
Is sleeping on the ground in cold weather better than on an air mattress?
Suspicious crontab entry running 'xribfa4' every 15 minutes
What can I do to avoid potential charges for bribery?
Calculate the shadow on earth of a large orbital disk
What is a terminal plane in high frequency circuits?
Why is it so hard to land on the Moon?
SSH from a shared workplace computer
Drawing Super Mario Bros.....in LaTeX
A variant of the Shortest Path Problem
Can the bass be used instead of drums?
70's/80's story about a high ranking prisoner of war on a prison planet
What is the word for things that work even when they aren't working - e.g escalators?
A demigod among men
How can I make "acts of patience" exciting?
Numbering like equations for regular text
A Society Built Around Theft?
Fill a bowl with alphabet soup
If Wish fails, do you suffer the 33% chance to be unable to cast wish ever again?
I didn't do any exit passport control when leaving Japan. What should I do?
UK PM is taking his proposal to EU but has not proposed to his own parliament - can he legally bypass the UK parliament?
Why is lying to Congress a crime?
How to execute a project with two resources where you need three resources?
Transferring 9 pegs on a 9x9 grid
Professor Halfbrain and the 9x9 chessboard (Part 2)A Puzzling GridReassembling the Marquetry II: The Coffee Table Strikes BackDoes this mathy square have any solutions? (And how many?)Place 4x12 detainees on a 7x7 grid of cellsIntroducing: Sudoku-JanpuThe very special matrixSolving a Rullo PuzzlePainting a 4x6 grid with 2 coloursPaint 10 cells of a 10x10 grid
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty
margin-bottom:0;
.everyonelovesstackoverflowposition:absolute;height:1px;width:1px;opacity:0;top:0;left:0;pointer-events:none;
$begingroup$
You are given a 9x9 grid with a set of 9 pegs (red circles) arranged in a 3x3 pattern in the corner, as shown below:
A peg can jump over another adjacent peg in any direction (horizontal, vertical or diagonal as shown in blue), provided that the destination cell is empty. A move consists of taking one peg and making one or more consecutive jumps, as shown below:
Can you transfer all the 9 pegs to the opposite corner of the grid, arranged in the same 3x3 pattern?
Bonus question: what is the smallest number of moves you can do it in?
Good luck!
mathematics combinatorics
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
$endgroup$
|
show 1 more comment
$begingroup$
You are given a 9x9 grid with a set of 9 pegs (red circles) arranged in a 3x3 pattern in the corner, as shown below:
A peg can jump over another adjacent peg in any direction (horizontal, vertical or diagonal as shown in blue), provided that the destination cell is empty. A move consists of taking one peg and making one or more consecutive jumps, as shown below:
Can you transfer all the 9 pegs to the opposite corner of the grid, arranged in the same 3x3 pattern?
Bonus question: what is the smallest number of moves you can do it in?
Good luck!
mathematics combinatorics
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
$endgroup$
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
2
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago
|
show 1 more comment
$begingroup$
You are given a 9x9 grid with a set of 9 pegs (red circles) arranged in a 3x3 pattern in the corner, as shown below:
A peg can jump over another adjacent peg in any direction (horizontal, vertical or diagonal as shown in blue), provided that the destination cell is empty. A move consists of taking one peg and making one or more consecutive jumps, as shown below:
Can you transfer all the 9 pegs to the opposite corner of the grid, arranged in the same 3x3 pattern?
Bonus question: what is the smallest number of moves you can do it in?
Good luck!
mathematics combinatorics
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
$endgroup$
You are given a 9x9 grid with a set of 9 pegs (red circles) arranged in a 3x3 pattern in the corner, as shown below:
A peg can jump over another adjacent peg in any direction (horizontal, vertical or diagonal as shown in blue), provided that the destination cell is empty. A move consists of taking one peg and making one or more consecutive jumps, as shown below:
Can you transfer all the 9 pegs to the opposite corner of the grid, arranged in the same 3x3 pattern?
Bonus question: what is the smallest number of moves you can do it in?
Good luck!
mathematics combinatorics
mathematics combinatorics
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
edited 17 hours ago
Dmitry Kamenetsky
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
asked 17 hours ago
Dmitry KamenetskyDmitry Kamenetsky
1,6692 silver badges27 bronze badges
1,6692 silver badges27 bronze badges
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
2
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago
|
show 1 more comment
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
2
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
2
2
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago
|
show 1 more comment
2 Answers
2
active
oldest
votes
$begingroup$
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can be moved to the bottom right corner.
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
$endgroup$
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
add a comment
|
$begingroup$
It's possible.
Assume the pegs are in the upper left corner of a slightly enlarged chess board, which has indices $1 - 9$ and A - I. Now make the moves
b8-d6, c7-e5, d6-f4, e5-g3, f4-h2, g3-i1
b9-d7, c9-c7, c8-e6, c7-e7, d7-f5, e7-e5, e6-g4, e5-c5, f5-h3, g5-g3, g4-i2, g3-i3
a7-c7, a9-a7, a8-c6, c7-c5, a7-c7, b7-d5, c5-e5, c7-c5, c6-e4, e5-e3, c5-e5, d5-f3, e3-g3, e5-e3, e4-g2, g3-g1, e3-g3, f3-h1
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
$endgroup$
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/4.0/"u003ecc by-sa 4.0 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%2f89765%2ftransferring-9-pegs-on-a-9x9-grid%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can be moved to the bottom right corner.
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
$endgroup$
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
add a comment
|
$begingroup$
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can be moved to the bottom right corner.
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
$endgroup$
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
add a comment
|
$begingroup$
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can be moved to the bottom right corner.
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
$endgroup$
I was having a slow work day, so I fired up Blender and made this:
In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can be moved to the bottom right corner.
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
answered 7 hours ago
squeamish ossifragesqueamish ossifrage
8,7304 gold badges32 silver badges44 bronze badges
8,7304 gold badges32 silver badges44 bronze badges
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
add a comment
|
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
2
2
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
$begingroup$
((((worship))))
$endgroup$
– Conifers
7 hours ago
1
1
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
That is so beautiful!
$endgroup$
– Dmitry Kamenetsky
1 hour ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
$begingroup$
If consecutive moves by the same piece count as a single move, you could probably optimize this some. (Looks great though.)
$endgroup$
– Darrel Hoffman
17 mins ago
add a comment
|
$begingroup$
It's possible.
Assume the pegs are in the upper left corner of a slightly enlarged chess board, which has indices $1 - 9$ and A - I. Now make the moves
b8-d6, c7-e5, d6-f4, e5-g3, f4-h2, g3-i1
b9-d7, c9-c7, c8-e6, c7-e7, d7-f5, e7-e5, e6-g4, e5-c5, f5-h3, g5-g3, g4-i2, g3-i3
a7-c7, a9-a7, a8-c6, c7-c5, a7-c7, b7-d5, c5-e5, c7-c5, c6-e4, e5-e3, c5-e5, d5-f3, e3-g3, e5-e3, e4-g2, g3-g1, e3-g3, f3-h1
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
$endgroup$
add a comment
|
$begingroup$
It's possible.
Assume the pegs are in the upper left corner of a slightly enlarged chess board, which has indices $1 - 9$ and A - I. Now make the moves
b8-d6, c7-e5, d6-f4, e5-g3, f4-h2, g3-i1
b9-d7, c9-c7, c8-e6, c7-e7, d7-f5, e7-e5, e6-g4, e5-c5, f5-h3, g5-g3, g4-i2, g3-i3
a7-c7, a9-a7, a8-c6, c7-c5, a7-c7, b7-d5, c5-e5, c7-c5, c6-e4, e5-e3, c5-e5, d5-f3, e3-g3, e5-e3, e4-g2, g3-g1, e3-g3, f3-h1
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
$endgroup$
add a comment
|
$begingroup$
It's possible.
Assume the pegs are in the upper left corner of a slightly enlarged chess board, which has indices $1 - 9$ and A - I. Now make the moves
b8-d6, c7-e5, d6-f4, e5-g3, f4-h2, g3-i1
b9-d7, c9-c7, c8-e6, c7-e7, d7-f5, e7-e5, e6-g4, e5-c5, f5-h3, g5-g3, g4-i2, g3-i3
a7-c7, a9-a7, a8-c6, c7-c5, a7-c7, b7-d5, c5-e5, c7-c5, c6-e4, e5-e3, c5-e5, d5-f3, e3-g3, e5-e3, e4-g2, g3-g1, e3-g3, f3-h1
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
$endgroup$
It's possible.
Assume the pegs are in the upper left corner of a slightly enlarged chess board, which has indices $1 - 9$ and A - I. Now make the moves
b8-d6, c7-e5, d6-f4, e5-g3, f4-h2, g3-i1
b9-d7, c9-c7, c8-e6, c7-e7, d7-f5, e7-e5, e6-g4, e5-c5, f5-h3, g5-g3, g4-i2, g3-i3
a7-c7, a9-a7, a8-c6, c7-c5, a7-c7, b7-d5, c5-e5, c7-c5, c6-e4, e5-e3, c5-e5, d5-f3, e3-g3, e5-e3, e4-g2, g3-g1, e3-g3, f3-h1
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
answered 8 hours ago
JensJens
7553 silver badges9 bronze badges
7553 silver badges9 bronze badges
add a comment
|
add a comment
|
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%2f89765%2ftransferring-9-pegs-on-a-9x9-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
$begingroup$
@Bass that's a good point. I don't think it would be possible to show optimality without a computer. However, I was hoping that people can still do this by hand and get sub-optimal answers. Would that still be ok for a puzzle? Perhaps I need to reword the question somehow?
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Ok I've modified the problem. The primary objective is to complete the puzzle in any number of moves. The bonus question asks for the minimal number of moves.
$endgroup$
– Dmitry Kamenetsky
17 hours ago
$begingroup$
Can't I just diagonally shift all pegs in 9×6= 54 moves.
$endgroup$
– Rishi
16 hours ago
$begingroup$
@Rishi sorry I don't understand your solution. They need to jump, not shift.
$endgroup$
– Dmitry Kamenetsky
16 hours ago
2
$begingroup$
@Rishi Pegs must always jump over other pegs.
$endgroup$
– Jaap Scherphuis
15 hours ago