There are many kinds of good problems, not just ones involving complicated maths and physics calculations. So, this month, it's Chess Month! Here's the first one:
- What should white do?
- We can't avoid adding a little bit of maths after all. Think of the chessboard as a mathematical pattern. Each point on the board is either black or white. The colours are equivalent; in other words, if you invert the colours and rotate the board, you get the same thing. The length of the side of a square is 1, and there are no points outside the squares. Now, imagine drawing a line so that every point on the line is white. What is the upper limit for the length of such a line?
- Is there any maximum length at all?
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