2. The item cost 64 rubles. Once a month, its price changed by $50\%$ either increasing or decreasing. It is known that over the course of six months, the price increased three times and decreased three times (the order in which this happened is unknown). Can the final price of the item after six months be determined uniquely? If so, what did it become?
Answer: Yes; the item will cost 27 rubles.

Solution. An increase of $50\%$ means that the current price is multiplied by $3/2$, and a decrease of $50\%$ means that the current price is multiplied by $1/2$. Therefore, regardless of the order in which the price increased or decreased, the price of the sofa after six months will be $64 \cdot (3/2)^3 \cdot (1/2)^3 = 27$ rubles.

Evaluation. If only some specific cases are considered and the correct numerical answer is obtained, 4 points. For a complete solution, 12 points.