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 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?
 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?

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Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0do u need explanation

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3What does repaint mean? Invert the colours of a row? (IE turn all light squares dark and vice versa)

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0ok suppose that we want one black square that is how we can do it

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0black square is in the middle lets say at 4rth row and 4rth coloumn

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0first we paint all the rows except 4rth one with white color not 4rth row 4rth row must have one black

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0then we paint all coloumns with white except 4rth coloumn

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3So, in simple terms, repainting is a function that maps... dw:1370257845631:dw

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0in 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

Fazeelayaz
 one year ago
Best ResponseYou've already chosen the best response.0ok 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

Ishaan94
 one year ago
Best ResponseYou've already chosen the best response.0I guess so @terenzreignz , because the answer at back is 'no'.

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3Well 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

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3Let's repaint the 1st, 3rd, 5th and 7th rows (starting from the top) 1&0&1&0&1&0&1&0 \[\large \left[\begin{matrix}1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\\1&0&1&0&1&0&1&0\end{matrix}\right]\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3Okay, nvm, I lost myself :D

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3It 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...

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.3Though you could always repaint the second, fourth, sixth, and eight columns (from the left) and end up with one (really big) dark square XD
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