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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.

What fraction of the cheese is left?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.*