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Ishaan94
 2 years 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?
Ishaan94
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0do u need explanation

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

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

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

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

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

terenzreignz
 2 years 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
 2 years 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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