1. ## Problem Solving (Digits)

How many positive integers under 1000 use only the digits 0, 1, 2 when written?

2. Use all 3 digits? Like, 102 would be lowest, 201 highest?

Or do you mean: 1,2,10,11,12,20,21,22 ...... 221,222?

3. Hello, matgrl!

How many positive integers under 1000 use only the digits 0, 1, 2 when written?

I assume that leading zeros are not allowed.

We could write them out and count them . . . The answer is 26.

We can reason it out like this . . .

There are only 2 one-digit numbers: 1 and 2.

For two-digit numbers: there are 2 choices for the first digit
. . and 3 choices for the second.
There are: $\displaystyle 2 \times 3 \,=$ 6 two-digit numbers.

For three-digit numbers: there are 2 choices for the first digit,
. . 3 choices for the second,
. . and 3 choices for the third.
There are: $\displaystyle 2 \times 3 \times 3 \,=$ 18 three-digit numbers.

Therefore, there are: .$\displaystyle 2 + 6 + 18 \:=\:26$ such numbers.

4. three digits

5. actually I think it might be 2*2*1 meaning there s only 4 choices.

6. If leading 0 allowed, then 6:
012
021
102
120
201
210
If not, then 4