list all the 3 digit numbers that fit these clues. the hundreds digits is less than 3. the tens digit is less than 2. the ones digit is greater than 7

216

(1,2)(0,1)(8,9)

Looks like there are eight of them. So, list them.

To list all the 3-digit numbers that fit the given clues:

1. Start with the first clue: the hundreds digit is less than 3.

Numbers that satisfy this clue are 100, 101, 102, 103, 104, 105, 106, 107, 108, and 109.

2. Move to the second clue: the tens digit is less than 2.

Numbers that satisfy both the first and second clues are 100, 101, 102, 103, 104, 105, 106, 107, 108, and 109.

3. Proceed to the third clue: the ones digit is greater than 7.

Numbers that satisfy all three clues are 108 and 109.

Therefore, the 3-digit numbers that fit all the given clues are 108 and 109.

To find all the 3-digit numbers that fit these clues, we'll need to consider the range of possible values for each digit and then combine them.

1. The hundreds digit must be less than 3.
The possible values for the hundreds digit are 0, 1, and 2.

2. The tens digit must be less than 2.
The possible values for the tens digit are 0 and 1.

3. The ones digit must be greater than 7.
The possible values for the ones digit are 8 and 9.

Now let's combine the possible values for each digit to get the 3-digit numbers that satisfy the given clues:

- Numbers with hundreds digit 0: 087, 088, 089, 097, 098, 099 (6 numbers)
- Numbers with hundreds digit 1: 187, 188, 189, 197, 198, 199 (6 numbers)
- Numbers with hundreds digit 2: 287, 288, 289, 297, 298, 299 (6 numbers)

Adding up these numbers, we have a total of 18 three-digit numbers that fit the given clues: 087, 088, 089, 097, 098, 099, 187, 188, 189, 197, 198, 199, 287, 288, 289, 297, 298, and 299.