Jirka collects signatures of famous athletes and singers. He has a special notebook for this purpose and has decided that signatures will be on the front side of each page only. He numbered all these pages as $1,3,5,7,9, \ldots$, to know if any page gets lost. He wrote a total of 125 digits.

- How many pages did his notebook have?
- How many ones did he write in total?
There are five single-digit odd numbers. There are a total of $99-9=$ $=90$ two-digit numbers, of which 45 are odd. With these numbers, Jirka could number $5+45=50$ pages and would use $5+2 \cdot 45=95$ digits. There are still $125-95=30$ digits left to use. These exactly correspond to the first ten three-digit odd numbers from 101 to 119. Jirka numbered a total of $5+45+10=60$ pages, so the notebook has 60 sheets.

The digit 1 appears in the units place a total of twelve times (once in each ten: $1,11, \ldots$, $91,101,111$). In the tens place, the digit 1 appears ten times (five times among the numbers 11 to 19 and five times among 111 to 119). In the hundreds place, the digit 1 also appears ten times (exactly ten three-digit numbers were written). Jirka wrote a total of $12+10+10=32$ ones.

Evaluation. 3 points for each part of the problem. (The problem can also be solved by sequentially listing and counting the digits.)