The thief Rumcajs is teaching Cipísek to write numbers. They started writing from one and wrote consecutive natural numbers. Cipísek didn't find it very entertaining and pleaded for them to stop. Rumcajs eventually gave in and promised that he would stop writing as soon as Cipísek had a total of 35 zeros in the written numbers. Which number will Cipísek write as the last one? (M. Krejčová)
By writing down single-digit numbers, we obtain no zeros.

Two-digit numbers containing a zero are:

$$
10,20, \ldots, 90 \quad 9 \text{ zeros}
$$

Three-digit numbers containing a zero are:

| 100 | 2 zeros | (total 11 zeros) |
| :--- | :--- | :--- |
| $101,102, \ldots, 109$ | 9 zeros | (total 20 zeros) |
| $110,120, \ldots, 190$ | 9 zeros | (total 29 zeros) |
| 200 | 2 zeros | (total 31 zeros) |
| $201,202,203,204$ | 4 zeros | (total 35 zeros) |

Chippy wrote the number 204 as the last number.

Another solution. We sequentially write down the numbers that contain at least one zero. In parentheses after each number, the total number of zeros written so far is indicated, up to and including the relevant number.

10 (1), 20 (2), 30 (3), 40 (4), 50 (5), 60 (6), 70 (7), 80 (8), 90 (9), 100 (11), 101 (12), 102 (13), 103 (14), 104 (15), 105 (16), 106 (17), 107 (18), 108 (19), 109 (20), 110 (21), 120 (22), 130 (23), 140 (24), 150 (25), 160 (26), 170 (27), 180 (28), 190 (29), 200 (31), 201 (32), 202 (33), 203 (34), 204 (35).

Chippy's last written number was 204.

Evaluation. 1 point for determining the number of zeros in numbers 1 to 99; 4 points for the counts of zeros in three-digit numbers; 1 point for the insight that the 35th zero is in the number 204.

If a solver overlooks any zero, deduct a point; if there are multiple such oversights, award no more than 4 points.