Problem 1. A four-digit number is called wonderful if it is divisible by 25, the sum of its digits is divisible by 25, and the product of its digits is divisible by 25. Find all wonderful numbers.
Answer: 5875 and 8575.

Solution. The sum of the digits of a four-digit number does not exceed 36, so for a wonderful number, it must be equal to 25.

Since the wonderful number is divisible by 25, it ends in either 00, 50, 25, or 75.

If a four-digit number ends in 00 or 50, then the sum of its digits does not exceed $9+9+5=23$, which does not suit us.

If the wonderful number ends in 25, then the sum of the first two digits must be 18. In this case, it can only be the number 9925, but the product of its digits is not divisible by 25.

Therefore, the wonderful number can only end in 75. In this case, the sum of the first two digits is 13, and their product must be divisible by 5. Then these two digits are 5 and 8 (in any order).

Criteria

4 p. A complete and justified solution is provided.

0 6. The problem is not solved or is solved incorrectly.

## In other cases, sum the following criteria:

1 p. It is proven that the sum of the digits of a four-digit wonderful number is 25.

1 6. It is proven that a four-digit wonderful number cannot end in 00 or 50.

1 6. It is proven that a four-digit wonderful number cannot end in 25.

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