if all the numbers from 1 to 2013 are written down how many of these will have two or more zeroes next to each other

To solve this problem, we need to count the numbers from 1 to 2013 that have two or more zeroes next to each other.

One way to approach this is by analyzing the pattern of numbers and identifying the conditions for having two or more zeroes together.

We can start by counting the single zero numbers:

- There are 10 single-digit numbers (0 to 9), of which only 1 number (0) has two zeroes together.
- In the range of two-digit numbers (10 to 99), all of them have a zero in the units place, resulting in 10 numbers with two zeroes together.

Next, we move on to three-digit numbers to see how many have two or more zeroes together. We can break it down into cases:

1. Numbers ending with two zeroes: There are 201 three-digit numbers ending with two zeroes (100, 200, 300, ..., 2000, 2010, ..., 2010).

2. Numbers with a single zero in the units place: In this case, we have 100 possible numbers between 100 to 199, and 100 possible numbers between 1000 to 1099.

3. Numbers with a single zero in the tens place: We have 10 possible numbers for each position of the zero, resulting in a total of 20 numbers (110, 120, ..., 190, 210, 220, ..., 290, ..., 2010, 2020, ..., 2090).

Therefore, the total count of numbers with two or more zeroes together from 1 to 2013 is: 1 + 10 + 201 + 100 + 20 = 332.

So, there are 332 numbers from 1 to 2013 that have two or more zeroes next to each other.