Question 130
A cat from a neighboring village goes to Butale to tease the village dogs. Every night, when everyone is asleep, he sneaks into Butale, squeals at the top of his voice, and then drags her back home. When the cat purrs, all dogs within $90~\mathrm{m}$ will bark. Since Butale is a small village, every 2 dogs in the village are $100~\mathrm{m}$ away from each other. Can the cat position itself so that all the village dogs bark at it at the same time?