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- #1

- Mar 10, 2012

- 835

I am having trouble with the following quesion.

Let $R=\{(x,y)\in\mathbb R^2:A\leq x\leq B, C\leq y\leq D\}$ be a rectangle in $\mathbb R^2$ which can be covered (overlapping allowed) with $25$ discs of radius $1$ each.

Then $R$ can be covered with $101$ rectangles of radius $1/2$ each.

I think the question is wrong. I think that a rectangle having one side $1.01$ units and the other side just long enough so that $25$ discs of radius $1$ units can cover it will not be coverable by 101 discs of radius $1/2$.

I don't know how to prove this.

Can anybody help?