# Task 9.1

All three-digit numbers are written in a row: $100101102 \ldots 998$ 999. How many times in this row does a zero follow a two?

## Number of points 7  Answer:  19

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# Solution

Since a three-digit number cannot start with zero, the two followed by a zero cannot be in the units place of any three-digit number in the sequence. Let's assume the two is in the tens place of a three-digit number. Then the zero following it is in the units place of the same number, i.e., the number ends in 20. There are 9 such numbers: 120, 220, ..., 920. Finally, if the two followed by a zero is in the hundreds place, then the corresponding three-digit number starts with 20. There are 10 such numbers: 200, 201, ..., 209. Therefore, the zero will follow the two 19 times in total.