How many numbers between 100 and 300 begin or end with 2?

It's probably easier to first count the total numbers and then subtract the ones that *don't* start or end with 2.

Let's actually focus on the numbers 100 to 299. That's 200 numbers.

The first digit can be 1 or 2, but only 1 works to not have a starting digit of 2.

1 choice for the first digit.

The second digit can be anything (0 to 9)

10 choices for the second digit.

The third digit can be anything except 2 (0, 1, 3, ..., 9)

9 choices for the third digit.

So multiplying everything out:

1 * 10 * 9 = 90 numbers that don't start or end with 2.

That leaves 110 numbers that *do* start or end with 2.

If you want to enumerate them:

102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 200, 201, 202, ..., 298, 299

Answer:

110 numbers

Somewhere between several and numerous.

The number of  numbers between 100 and 300 

which begin or end with 2 is 110.

There are infinity such numbers, for example:

100.2

100.02

100.002

100.0002

etc.

If you mean "integers" instead of "numbers," the answer is 110.

Note that all numbers between 200 and 299, inclusive, begin or end with two. This is a total of 100 numbers.

Finally, the numbers between 100 and 200, not including 200, can't begin with two. Thus, we consider only numbers that can end in two. There are only ten such numbers. Namely they are: 102, 112, 122, 132, ..., 192.

Thus, there is a total of 110 numbers between 100 and 300 that begin or end with two.

Between 100 & 199, the first digit has to be one, second digit has ten possibilities, and the third digit has to be 2.  That's ten possibilities.

Between 200 & 299, there are 100 possibilities.

110.