1. Kolya came up with an entertainment for himself: he rearranges the digits in the number 2015, then places a multiplication sign between any two digits and calculates the value of the resulting expression. For example: $150 \cdot 2=300$, or $10 \cdot 25=250$. What is the largest number he can get as a result of such a calculation?
Answer: 1050

Solution. Note three facts (their justification is obvious). First, in the case of the maximum product, the digits in each of the factors are in descending order. That is, 0 should be at the end of one of the factors. Second, it does not matter at the end of which of the two factors to place 0, the product will not change. Therefore, it can be rearranged so that both factors become two-digit numbers. After that, only 3 options remain to be considered:

$$
21 \cdot 50=1050, \quad 52 \cdot 10=520, \quad 51 \cdot 20=1020
$$

Criteria.

## $(-)$

(-.) Correct answer with an example. It is not explained why it is correct.

$(-/+)$ A significant number of cases are missing

(+/2) It is stated that only half of the cases need to be considered (for example, the case of a three-digit and a one-digit number), but the explanation is unsatisfactory

$(+/-)$ 1-2 cases are missing

$(+$.

$(+)$ Correct answer with a review of all cases.