Find the number of times digit (1) is used while writing numbers from  1 to 100.

To find the number of times digit 1 is used while writing numbers from 1 to 100, we can break down the problem into three parts:

1. Count the number of times 1 appears in the tens place.
2. Count the number of times 1 appears in the ones place.
3. Add the two counts together.

Let's start with the first part:

1. Count the number of times 1 appears in the tens place:

In the range from 1 to 100, the tens digit is 1 for ten numbers: 10, 11, 12, ..., 19. So, 1 appears 10 times in the tens place.

Now, let's move to the second part:

2. Count the number of times 1 appears in the ones place:

In every set of ten numbers (1-10, 11-20, 21-30, ..., 91-100), 1 appears once in the ones place. Since there are ten sets of ten numbers from 1 to 100, 1 appears 10 times in the ones place.

Finally, let's add the two counts together:

3. Add the two counts together:

The number of times 1 appears in the tens place (10 times) plus the number of times 1 appears in the ones place (10 times) equals 20 times.

So, the digit 1 is used 20 times when writing the numbers from 1 to 100.