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A rectangular table has coins of unit radius placed on it (a coin counts as placed on the table as long as its center lies on the table; it may hang over the edge). No two coins overlap, and it is impossible to place any more coins on the table without causing an overlap. Given that such a configuration exists, is it always possible to place coins of unit radius, now allowed to overlap, so that they completely cover the table?
Covering means that for every point on the table there is a coin above it. The coins form a new arrangement; they do not have to include the original .