Puzzle time - cover the square with circles
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Suppose you have a unit square. If you also have four identical circles that can overlap, they would need to have a radius of 0.25·√2 to completely cover the square, as shown:
Now suppose that, instead of four identical circles, you have five identical circles that can overlap. What is the minimum radius they would need to completely cover a unit square?
Extra credit: Suppose you have six identical circles that can overlap. What is the minimum radius they would need to completely cover a unit square?