4. At Ivanov's house, there stands an odd three-digit number. The digit in the tens place is twice as large as the digit in the units place. The digit in the hundreds place is the sum of the digits in the tens and units places. Determine all possibilities for Ivanov's house number that is divisible by 9.
4. At Ivanov's house, there stands an odd three-digit number. The tens digit is twice as large as the units digit. The hundreds digit is the sum of the tens and units digits. Determine all possibilities for Ivanov's house number that is divisible by 9.

## Solution.

At Ivanov's house, the number is odd, so we conclude that the units digit can be 1, 3, 5, 7, or 9. 1 POINT The tens digit is twice as large as the units digit, and the hundreds digit is the sum of the tens and units digits, so we have two possibilities:

Units digit 1, tens digit 2, hundreds digit 3, i.e., the number 321.

1 POINT

Units digit 3, tens digit 6, hundreds digit 9, i.e., the number 963.

1 POINT

If the units digit were 5, 7, or 9, then the tens digit would be 10, 14, or 18, which is impossible.

1 POINT

Since Ivanov's house number is divisible by 9, the correct number is 963. 2 POINTS

TOTAL 6 POINTS

Note: A student who does not consider and reject the possibility of the units digit being 5, 7, or 9 can achieve a maximum of 5 POINTS.