A1 Ty took a positive number, squared it, then divided it by 3 , then cubed it, and finally divided it by 9 . In the end he received the same number as he started with. What was the number?
Answer: 3
Solution:
Assume Ty started with the number $x$. After squaring it and dividing by 3 , he will get the number $\frac{x^{2}}{3}$. After cubing this number and dividing by 9 , he will get the number
$$
\frac{\left(\frac{x^{2}}{3}\right)^{3}}{9}=\frac{\left(\frac{x^{6}}{3^{3}}\right)}{9}=\frac{x^{6}}{3^{5}} .
$$

We thus get that $x=\frac{x^{6}}{3^{5}}$, and after dividing both sides by $x$ and multiplying both sides by $3^{5}$, we get $x^{5}=3^{5}$, and so $x=3$.