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9

1

$begingroup$

There is $5$x$5$ equidistance matrix dot given as below;

You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end.

So what is the least number of dots you need to remove where forming a square by drawing lines between dots will be impossible?

Clarification: Dots need to be vertices of a square.

logical-deduction geometry

share|improve this question

edited 6 hours ago

Oray

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I interpreted this as "impossible to pick four dots that form a square", is this what is intended? (The way the puzzle is now written, it would also be possible to pick 8 points, and connect them pairwise with 4 lines that intersect so that the lines form a square)
  $endgroup$
  – Bass
  8 hours ago
  

  
  
  
  

add a comment | 

9

1

$begingroup$

There is $5$x$5$ equidistance matrix dot given as below;

You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end.

So what is the least number of dots you need to remove where forming a square by drawing lines between dots will be impossible?

Clarification: Dots need to be vertices of a square.

logical-deduction geometry

share|improve this question

edited 6 hours ago

Oray

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I interpreted this as "impossible to pick four dots that form a square", is this what is intended? (The way the puzzle is now written, it would also be possible to pick 8 points, and connect them pairwise with 4 lines that intersect so that the lines form a square)
  $endgroup$
  – Bass
  8 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

There is $5$x$5$ equidistance matrix dot given as below;

You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end.

So what is the least number of dots you need to remove where forming a square by drawing lines between dots will be impossible?

Clarification: Dots need to be vertices of a square.

logical-deduction geometry

share|improve this question

edited 6 hours ago

Oray

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

$endgroup$

share|improve this question

edited 6 hours ago

Oray

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

share|improve this question

edited 6 hours ago

Oray

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

asked 8 hours ago

OrayOray

17.2k44 gold badges3939 silver badges172172 bronze badges

3 Answers
3

active

oldest

votes

7

$begingroup$

Here's one with 10 dots removed. I tried for a long time to find one with 9, but I didn't succeed.

share|improve this answer

edited 5 hours ago

answered 8 hours ago

TedTed

18166 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  This still has a diagonal square that I can see (if columns are ABCDE, and rows are 12345 going down, it's formed by A3, C2, D4, B5)
  $endgroup$
  – StephenTG
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Still at least one square at A2, B5, E4, D1
  $endgroup$
  – Bass
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Still 3 left at D4-E3-C4-B2, A3-B1-D2-C4 and B5-A2-D1-E4
  $endgroup$
  – Belhenix
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I feel someone should point out that all of the comments above this one (that point out errors) no longer apply now that the answer has been edited. This solution now appears to be 100% correct (but now removes 10 dots instead of the previous 9)
  $endgroup$
  – plasticinsect
  4 hours ago
  

  
  
  
  

add a comment | 

3

$begingroup$

Here's an answer with the removal of

$11$ dots

Answer

If we interpret the question as Bass did, then I think we can remove

$13$ dots

Answer to Bass' version

share|improve this answer

edited 6 hours ago

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  row 4 col 3 could be added back, no?
  $endgroup$
  – jafe
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe I was answering the question as clarified by Bass. If we add this point back then the horizontal and vertical lines through it are achievable which together with the horizontal and vertical lines through point (2,5) would form a square.
  $endgroup$
  – hexomino
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe Oray had commented confirming Bass' assumption but has since deleted the comment.
  $endgroup$
  – hexomino
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  this is a valid answer, but not the least number of dots to remove.
  $endgroup$
  – Oray
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Oray Is Bass' interpretation correct?
  $endgroup$
  – hexomino
  6 hours ago
  

  
  
  
  

 | 
show 1 more comment

2

$begingroup$

Since I cannot post pictures in a comment, here's my question in clearer terms:

Did I form a square by drawing lines between dots? (I know I did. Does it count, though?)

(For better visibility, I deviated from the apparent standard of using near-imperceptible shade changes, and marked the relevant dots with bell peppers instead.)

share|improve this answer

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I see your point with some peppers :D I put a clarification for that :) AS "dots need to be vertices of a square." but good point though.
  $endgroup$
  – Oray
  6 hours ago
  
  

  
  
  
  

add a comment | 

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7

$begingroup$

Here's one with 10 dots removed. I tried for a long time to find one with 9, but I didn't succeed.

share|improve this answer

edited 5 hours ago

answered 8 hours ago

TedTed

18166 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  This still has a diagonal square that I can see (if columns are ABCDE, and rows are 12345 going down, it's formed by A3, C2, D4, B5)
  $endgroup$
  – StephenTG
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Still at least one square at A2, B5, E4, D1
  $endgroup$
  – Bass
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Still 3 left at D4-E3-C4-B2, A3-B1-D2-C4 and B5-A2-D1-E4
  $endgroup$
  – Belhenix
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I feel someone should point out that all of the comments above this one (that point out errors) no longer apply now that the answer has been edited. This solution now appears to be 100% correct (but now removes 10 dots instead of the previous 9)
  $endgroup$
  – plasticinsect
  4 hours ago
  

  
  
  
  

add a comment | 

7

$begingroup$

Here's one with 10 dots removed. I tried for a long time to find one with 9, but I didn't succeed.

share|improve this answer

edited 5 hours ago

answered 8 hours ago

TedTed

18166 bronze badges

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  This still has a diagonal square that I can see (if columns are ABCDE, and rows are 12345 going down, it's formed by A3, C2, D4, B5)
  $endgroup$
  – StephenTG
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Still at least one square at A2, B5, E4, D1
  $endgroup$
  – Bass
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Still 3 left at D4-E3-C4-B2, A3-B1-D2-C4 and B5-A2-D1-E4
  $endgroup$
  – Belhenix
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I feel someone should point out that all of the comments above this one (that point out errors) no longer apply now that the answer has been edited. This solution now appears to be 100% correct (but now removes 10 dots instead of the previous 9)
  $endgroup$
  – plasticinsect
  4 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Here's one with 10 dots removed. I tried for a long time to find one with 9, but I didn't succeed.

share|improve this answer

edited 5 hours ago

answered 8 hours ago

TedTed

18166 bronze badges

$endgroup$

share|improve this answer

edited 5 hours ago

answered 8 hours ago

TedTed

18166 bronze badges

answered 8 hours ago

TedTed

18166 bronze badges

answered 8 hours ago

TedTed

18166 bronze badges

3

$begingroup$

Here's an answer with the removal of

$11$ dots

Answer

If we interpret the question as Bass did, then I think we can remove

$13$ dots

Answer to Bass' version

share|improve this answer

edited 6 hours ago

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  row 4 col 3 could be added back, no?
  $endgroup$
  – jafe
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe I was answering the question as clarified by Bass. If we add this point back then the horizontal and vertical lines through it are achievable which together with the horizontal and vertical lines through point (2,5) would form a square.
  $endgroup$
  – hexomino
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe Oray had commented confirming Bass' assumption but has since deleted the comment.
  $endgroup$
  – hexomino
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  this is a valid answer, but not the least number of dots to remove.
  $endgroup$
  – Oray
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Oray Is Bass' interpretation correct?
  $endgroup$
  – hexomino
  6 hours ago
  

  
  
  
  

 | 
show 1 more comment

3

$begingroup$

Here's an answer with the removal of

$11$ dots

Answer

If we interpret the question as Bass did, then I think we can remove

$13$ dots

Answer to Bass' version

share|improve this answer

edited 6 hours ago

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  row 4 col 3 could be added back, no?
  $endgroup$
  – jafe
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe I was answering the question as clarified by Bass. If we add this point back then the horizontal and vertical lines through it are achievable which together with the horizontal and vertical lines through point (2,5) would form a square.
  $endgroup$
  – hexomino
  7 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @jafe Oray had commented confirming Bass' assumption but has since deleted the comment.
  $endgroup$
  – hexomino
  7 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  this is a valid answer, but not the least number of dots to remove.
  $endgroup$
  – Oray
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Oray Is Bass' interpretation correct?
  $endgroup$
  – hexomino
  6 hours ago
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

Here's an answer with the removal of

$11$ dots

Answer

If we interpret the question as Bass did, then I think we can remove

$13$ dots

Answer to Bass' version

share|improve this answer

edited 6 hours ago

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

$endgroup$

share|improve this answer

edited 6 hours ago

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

answered 7 hours ago

hexominohexomino

57.4k55 gold badges164164 silver badges264264 bronze badges

2

$begingroup$

Since I cannot post pictures in a comment, here's my question in clearer terms:

Did I form a square by drawing lines between dots? (I know I did. Does it count, though?)

(For better visibility, I deviated from the apparent standard of using near-imperceptible shade changes, and marked the relevant dots with bell peppers instead.)

share|improve this answer

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I see your point with some peppers :D I put a clarification for that :) AS "dots need to be vertices of a square." but good point though.
  $endgroup$
  – Oray
  6 hours ago
  
  

  
  
  
  

add a comment | 

2

$begingroup$

Since I cannot post pictures in a comment, here's my question in clearer terms:

Did I form a square by drawing lines between dots? (I know I did. Does it count, though?)

(For better visibility, I deviated from the apparent standard of using near-imperceptible shade changes, and marked the relevant dots with bell peppers instead.)

share|improve this answer

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I see your point with some peppers :D I put a clarification for that :) AS "dots need to be vertices of a square." but good point though.
  $endgroup$
  – Oray
  6 hours ago
  
  

  
  
  
  

add a comment | 

$begingroup$

Since I cannot post pictures in a comment, here's my question in clearer terms:

Did I form a square by drawing lines between dots? (I know I did. Does it count, though?)

(For better visibility, I deviated from the apparent standard of using near-imperceptible shade changes, and marked the relevant dots with bell peppers instead.)

share|improve this answer

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

$endgroup$

share|improve this answer

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges

answered 6 hours ago

BassBass

35.5k44 gold badges8787 silver badges206206 bronze badges