2. Indicate the smallest number ending in 37 with the sum of its digits equal to 37 and divisible by 37.
Answer: 99937.

Solution. The number is the smaller, the fewer digits are required to write it. Two digits - these are the last two digits, their sum is 10. Therefore, the sum of the other digits is 27, and there are at least three of them, since the largest digit is 9. Thus, the number 99937 satisfies three of the four requirements. It remains to check that it is divisible by