Jump to content
BrainDen.com - Brain Teasers
  • 0

Connect the squares



Within the outlined rectangle and Using vertical and horizontal line segments as a chain connect the squares of the same color but do not let the chains that connect common squares cross. All white squares must be occupied.


Edited by BMAD
Link to comment
Share on other sites

3 answers to this question

Recommended Posts

  • 0

We have a 7x6 chessboard, so let's paint the squares black and white starting with black top-left square.

Observe, that a path always consists of squares with alternating colors.
Therefore each path connecting squares of different color has equal number of black and white squares,
and each path connecting two squares of the same color contains one more square in color of it's endpoints.
Observe, that blue and green endpoints are all black, while third path has it's endpoints of different colors (one white and one black).
Covering the whole chessboard with three such paths would mean that the chessboard has two black squares more than white.
But clearly black and white squares of the chessboard are equal in number, therefore such three paths cannot exist.

Link to comment
Share on other sites

  • 0

i'm not seeing any possible solution.


the top most square is whats the minimum absolute necessary.

the problem comes in with the two lettered squares. if i cover A with blue, i have no way of getting A and C in the left most pic. if i cover B, i either cant connect to my already existing chain, or can do so but skip a square or two.

if i cover neither A nor B; the green doesn't work. i cant cover both A, B and connect to my errant chain.

i can't wait to see the solution if there is one.

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.

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.


  • Recently Browsing   0 members

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