Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Ishaan94

  • one year ago

Assume an \(8\times 8\) chessboard with usual colouring. You may repaint all the squares of a row or column. The goal is to attain one black square. Possible?

  • This Question is Closed
  1. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  2. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think

  3. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do u need explanation

  4. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    What does repaint mean? Invert the colours of a row? (IE turn all light squares dark and vice versa)

  5. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok suppose that we want one black square that is how we can do it

  6. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    black square is in the middle lets say at 4rth row and 4rth coloumn

  7. Jack1
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  8. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first we paint all the rows except 4rth one with white color not 4rth row 4rth row must have one black

  9. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then we paint all coloumns with white except 4rth coloumn

  10. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    So, in simple terms, repainting is a function that maps... |dw:1370257845631:dw|

  11. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in this way all the remaining except the the one we said will be white and only one which is at location 4rth row and 4rth coloumn would be white

  12. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so ans is yes

  13. Fazeelayaz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok repainting means painting what you want to paint if 1 row is to be repainted with white then all the squares in that row would be white

  14. Ishaan94
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I guess so @terenzreignz , because the answer at back is 'no'.

  15. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Well then, \[\large \left[\begin{matrix}0&1&0&1&0&1&0&1 \\1&0&1&0&1&0&1&0\\0&1&0&1&0&1&0&1\\1&0&1&0&1&0&1&0\\0&1&0&1&0&1&0&1\\1&0&1&0&1&0&1&0\\0&1&0&1&0&1&0&1\\1&0&1&0&1&0&1&0\end{matrix}\right]\] Okay, let's start with this... 0 = light square 1 = dark square

  16. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Let's repaint the 1st, 3rd, 5th and 7th rows (starting from the top) 1&0&1&0&1&0&1&0 \[\large \left[\begin{matrix}1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\end{matrix}\right]\]

  17. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Okay, nvm, I lost myself :D

  18. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    It might the case that no matter how you repaint, you always add/subtract an even number of dark squares.... so you can't end up with just 1...

  19. terenzreignz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Though you could always repaint the second, fourth, sixth, and eight columns (from the left) and end up with one (really big) dark square XD

  20. Ishaan94
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's it.

  21. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.