3+ [Inequalities. Case Analysis] Pinocchio buried two ingots - a golden one and a silver one - on the Field of Wonders. On good weather days, the golden ingot increases by $30\%$, and the silver ingot by $20\%$. On bad weather days, the golden ingot decreases by $30\%$, and the silver ingot by $20\%$. After a week, it turned out that one of the ingots had increased, while the other had decreased. How many days was the weather good?
Increasing a number by $20 \%$ is equivalent to multiplying it by 1.2, and decreasing a number by $20 \%$ is equivalent to multiplying it by 0.8 (for $30 \%$ - by 1.3 and 0.7, respectively). Therefore, the result does not depend on the sequence of good and bad weather, but only on the number of good and bad days.

After one good and one bad day, both ingots decrease: $1.2 \cdot 0.81$, while $1.3^{4} \cdot 0.7^{3}<1$. On the other hand, after two good and one bad day, the gold ingot increases. Therefore, it also increases after four good and two bad days, and even more so after five good and two bad days. Thus, if there are five or more good days, the gold ingot grows. Therefore, only when there are four good days does one ingot grow while the other decreases.

## Answer

4 days.