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: Let's play... math
These are two problems in math:
1) Start with positive integers 1, 2, ... , 4n-1. In one move you may replace any two integers by their difference. Tell whether odd or even integer will be left after 4n-2 steps. How to prove it?
2) Assume an 8x8 chessboard with the usual coloring. You may repaint all squares of a row or a column (all white squares repainted in black and black in white along a row/column ). The goal is to attain just one black square ( that means one small square, not 2x2 or 8x8 square ). Can you reach the goal?
PS: These problems were taken from one problem set, so it's certain that they have at least one solution. Join the game, don't be shy (:
These are two problems in math:
1) Start with positive integers 1, 2, ... , 4n-1. In one move you may replace any two integers by their difference. Tell whether odd or even integer will be left after 4n-2 steps. How to prove it?
2) Assume an 8x8 chessboard with the usual coloring. You may repaint all squares of a row or a column (all white squares repainted in black and black in white along a row/column ). The goal is to attain just one black square ( that means one small square, not 2x2 or 8x8 square ). Can you reach the goal?
PS: These problems were taken from one problem set, so it's certain that they have at least one solution. Join the game, don't be shy (: