# How many 3 digit positive integers are there such that the average of two of the digits amongst them equal the third digit?

Table of Contents

- 1 How many 3 digit positive integers are there such that the average of two of the digits amongst them equal the third digit?
- 2 How many positive integers of at most 3 digits are there such that the product of their digits is 30?
- 3 How many numbers of at least 3 different digits can be formed using the integers 1 2 3 4 5?
- 4 How many hundreds digit integers are there that do not contain 5?
- 5 How many possibilities are there for 3 blank numbers?

## How many 3 digit positive integers are there such that the average of two of the digits amongst them equal the third digit?

Therefore, there are 9*10^(3–1) = 9*100 = 900 3-digit numbers. The smallest positive 3-digit number is 100, and the largest is 999. Good luck!

**How many three digit positive integers are there such that at least two of its digits are the same?**

. Thus, there are 252 numbers that are 3-digit numbers that have at least 2 digits that have the same value.

### How many positive integers of at most 3 digits are there such that the product of their digits is 30?

given abc=252. the possible options are (4,7,9)(4,9,7)(7,9,4)(7,4,9)(9,7,4)(9,4,7)(6,7,6) (6,6,7)(7,6,6) hence there are 9 possibilities.

**How many 3 digit numbers are there such that the difference between consecutive digits must be 3?**

Since if the middle number is 0, the only number that differs by 3 is 3, there is thus only one possible way, 303. Since if the middle number is 9, the only number that differs by 3 is 6, there is thus only one possible way, 696.

#### How many numbers of at least 3 different digits can be formed using the integers 1 2 3 4 5?

Ex: Given 1, 2, and 3, you could make 123, 132, 213, 231, 312, or 321. Plugging that entire expression above into the calculator gives you 156; there are 156 different numbers you could create from the set {1, 2, 3, 4, 5, 6} that are AT MOST 3 digits.

**How many odd positive 3 digit numbers are there?**

And for the first digits we can place digits in the range 1… 9 but we cannot place the digits that are used in the two other digits and we can place only 7 digits. However the result is not correct, because there are 320 odd three-digits numbers with different digits.

## How many hundreds digit integers are there that do not contain 5?

The correct is 288. My idea is, first I get the total number of 3-digit integers that do not contain 5, then divide it by 2. And because it is a 3-digit integer, the hundreds digit can not be zero.

**How many two digit numbers can be combined together?**

So, there are 9 two digit numbers that start with 1, 9 that start with 2, 9 that start with 3, and so on. So if we have 8 different first digits and 9 different second digits, they can be combined in 8*9 = 72 different ways.

### How many possibilities are there for 3 blank numbers?

The digit 5 is also not a possibility). Thus, 4 possibilities for blank 3. Now, using multiplication principle for all three blanks : 8*9*3 = 288. I think you meant 8*9*4 = 288 …but otherwise, you are correct!