Jump to content
BrainDen.com - Brain Teasers
  • 0

Square Free


TimeSpaceLightForce
 Share

Question

Remove 4 pieces from the above position.. then place them back on any free squares of the chessboard  so that no square can be formed by any four pieces on corners of a square .  Which pieces to choose and where to position them?

 

square chess.png

Spoiler

This is base on my posted question : " Anti Square" .About most number of pieces on chess board without forming a square. Yet 34 may not be the maximum.

 

Link to comment
Share on other sites

Recommended Posts

  • 1
16 hours ago, rocdocmac said:
  Reveal hidden contents

I have identified 7 squares on the board as it is currently. Correct? WrongI now have found 8

There are 19 pieces involved in these 7 squares. Correct? Wrong20 pieces involved.

 

Spoiler

I believe the 8 squares you've identified are the following:
{a1, c1, c3, a3},
{a1, e1, e5, a5},
{c1, h1, h6, c6},
{a3, d3, d6, a6},
{c3, h3, h8, c8},
{d3, g3, g6, d6},
{c3, d1, f2, e4},
{c3, e1, g3, e5}
If this is not correct, there are more than 8 squares.


 

Addendum:

16 hours ago, rocdocmac said:
  Reveal hidden contents

I have identified 7 squares on the board as it is currently. Correct? WrongI now have found 8

There are 19 pieces involved in these 7 squares. Correct? Wrong20 pieces involved.

 

Spoiler

The count of 20 pieces involved is wrong as there are 21 pieces involved in total in corners of these 8 squares:
{a1, c1, d1, e1, h1, f2,  a3, c3, d3, h3, g3, e4, a5,  e5, a6, c6,  d6, g6, h6, c8, h8}

.

Link to comment
Share on other sites

  • 0
22 hours ago, TimeSpaceLightForce said:
  Hide contents

Hint: Only remove the square corner pieces 

Spoiler

 

I have identified 7 squares on the board as it is currently. Correct?

There are 19 pieces involved in these 7 squares. Correct?

If you say that only the square corner pieces should be removed, does that mean pieces from only one square?

I think i have identified the four pieces. I can place three of them back without making extra squares, but I am battling placing the last one back! Think I'll go through my process again.

 

 

 

Edited by rocdocmac
Moved to spoiler
Link to comment
Share on other sites

  • 0
Spoiler

I myself did not own the 34 pieces solution. Someones code did it; like placing 3 marks randomly.. then one by one marking every square and  Tested if  it  is 4th corner or not..My original manual solution is just 31 pieces thats why I posted before using a chess set 32 pieces

 

Spoiler

There are  more  than 300 possible squares  on a chessboard.. i guess 

 

Link to comment
Share on other sites

  • 0
3 hours ago, rocdocmac said:
  Hide contents

Looks like there are even more perfect squares on the original layout!

My latest count is 11 squares with 27 pieces being involved and 11 of them found in more than one square.

Spoiler

 

My own count has also increased, both with squares and pieces.  12 squares and 28 pieces. The four additional squares are: {a6, c3, f5, d8}, {e5, d3, f2, g4}, {b2, c1, d2, c3}, {a5, d3, f6, c8} -- the previously listed being: {a1, c1, c3, a3},
{a1, e1, e5, a5}, {c1, h1, h6, c6}, {a3, d3, d6, a6}, {c3, h3, h8, c8}, {d3, g3, g6, d6}, {c3, d1, f2, e4}, {c3, e1, g3, e5}

The twenty-eight pieces are those at {a1, a3, a5, a6, b2, c1, c3, c6, c8, d1, d2, d3, d5, d6, d8, e1, e4, e5, f2, f5, f6, g3, g4, g6, h1, h3, h6, h8}.
Removing the two pieces at c3 and d3 will leave of these twelve squares but the two {a1, e1, e5, a5} and {c1, h1, h6, c6}. From each of these remaining two one of the four corners of each will also need to be removed.

 

 

 

Link to comment
Share on other sites

  • 0
1 hour ago, DejMar said:

 

Spoiler

The twenty-eight pieces are those at {a1, a3, a5, a6, b2, c1, c3, c6, c8, d1, d2, d3, d5, d6, d8, e1, e4, e5, f2, f5, f6, g3, g4, g6, h1, h3, h6, h8}.

 

Spoiler

There is no d5. Check again ... it should be 27 pieces!

 

 

Edited by rocdocmac
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...