## Task 3 - 300623

A book printing company has the following number of letters for printing the digits 0, 1, ..., 9:

| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Quantity | 350 | 340 | 320 | 340 | 360 | 310 | 300 | 320 | 320 | 340 |

Using only these letters, the page numbers from 1 to 1020 of a book are to be printed. No letter should be used more than once.

Are the letters sufficient for this purpose? Justify your answer!
The letters are not sufficient.

At the unit place, the digit 6 is used once for the numbers 1 to 10, 11 to 20, ..., 1011 to 1020, i.e., 102 times.

At the tens place, the digit 6 is used 10 times for the numbers 60 to 69, 160 to 169, ..., 960 to 969, i.e., 100 times.

At the hundreds place, the digit 6 is used for the numbers 600, ..., 699, i.e., 100 times.

Therefore, 302 letters with the digit 6 are used, while only 300 are available.