13. About the cat. A ribbon was stretched around the Earth along the equator. Then the length of the ribbon was increased by 1 meter and again evenly positioned around the equator. Will a cat be able to crawl through the resulting gap?
13. Let the radius of the Earth be $R$, and the formed gap be $h$, then $2 \pi(R+h)-2 \pi R=1$ and $2 \pi h=1$. Therefore, the size of the gap $h=\frac{1}{2 \pi} \approx 15$ cm - a gap quite sufficient for a cat to squeeze through.