9767 /www/nrich/html/content/id/9767/ 1 2013-01-04T16:31:59 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">The three blind mice stole a piece of cheese. In the night, the first mouse ate $\frac{1}{3}$ of the cheese. Later, the second mouse ate $\frac{1}{3}$ of the remaining cheese. Finally, the third mouse ate $\frac{1}{3}$ of what was then left of the cheese.<br></br> Between them, what fraction of the cheese did they eat?</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">After the first mouse has eaten, $\frac{2}{3}$ of the cheese remains. After the second mouse has eaten, $\frac{2}{3}$ of $\frac{2}{3}$, that is $\frac{4}{9}$, of the cheese remains. Finally, after the third mouse has eaten, $\frac{2}{3}$ of $\frac{4}{9}$, that is $\frac{8}{27}$ of the cheese remains. So the mice ate $\frac{19}{27}$ of the cheese.</mdoxml> 2 3 0 0 1 0 0 Weekly Problem 8 - 2013