Problem 3. Excellent students Alyosha and Vasya are listing four-digit numbers. Alyosha lists numbers where the first digit is equal to the product of the other three, while Vasya lists numbers where the last digit is equal to the product of the other three. Who will list more numbers and by how many?
Task 3. Excellent students Alyosha and Vasya write down four-digit numbers. Alyosha writes down numbers where the first digit is equal to the product of the other three, while Vasya writes down numbers where the last digit is equal to the product of the other three. Who will write down more numbers and by how many?

| Solution | Criteria |
| :--- | :--- |
| Since Vasya can write numbers that | 1. 1 point for the correct answer. |
| end in 0, while Alyosha cannot write | 2. 1 point if it is explained why Vasya will write |
| numbers that start with 0, Vasya will | more numbers. |
| write more numbers. Let's count the | 3. -2 points if the incorrect answer is given because 00 was counted twice. |
| number of four-digit numbers that end |  |
| in 0 and contain at least one more 0 in |  |
| their representation. The first digit of |  |
| such a four-digit number can be any digit |  |
| from 1 to 9. Zero must be on the second |  |
| or third place. The number of numbers of |  |
| the form 0right is 9, the number of numbers |  |
| of the form p0 is 9 (where p>0), and there is 00. |  |
| Therefore, the total number of such numbers |  |
| is $9 \times (9 + 9 + 1) = 171$. |