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How do I prove that it is possible to cover the whole plane with squares with side 1?

Please suggest different approaches to the above problem.

Thank you.

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Does it require proof? –  André Nicolas Nov 26 '11 at 5:10
In English, statements such as "Suggest different approaches" can read as orders, or at least as somewhat rude. The polite way is to ask as question. E.g., "Could someone suggest an approach to the problem above?" –  Arturo Magidin Nov 26 '11 at 5:12
You have asked several questions and not accepted any answers. Do you understand how accepting answers works? and how it's a good thing to do? –  Gerry Myerson Nov 26 '11 at 5:56

1 Answer 1

If you aren't concerned about overlap (which you don't mention in your statement), then for every point x in the plane, include a square of side length 1 whose lower lefthand corner is x. Not only is everything covered, but each point gets its own personal square.

If you'd like a slightly less silly cover, then anchor the lower lefthand corner of a square at each point with integer coordinates. If you remove the top side and right side of your square, then this scheme will cover the entire plane without overlap.

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