Table of Contents

- 1 How many numbers between 100 and 1000 are there that contain at least one of their digits as 7?
- 2 How many numbers are there between 100 to 1000 such that at least one of their digit is 6?
- 3 How many numbers are there between 100 and 1000 such that exactly one of their digits is 3 if repetition?
- 4 How many numbers are there between 1 and 1000?
- 5 How many numbers are there between 100 and 999?
- 6 How many numbers from 1 to 1000 are perfect squares and cubes?
- 7 How many numbers from 1 to 100 are there?
- 8 What is the number of 3 digit numbers from 100 to 999?

## How many numbers between 100 and 1000 are there that contain at least one of their digits as 7?

Hence, the numbers between 100 and 1000 having the digit 7 exactly once are 72 + 72 + 81 = 225.

### How many numbers are there between 100 to 1000 such that at least one of their digit is 6?

225 numbers

Thus, there are 225 numbers between 100 and 1000 that have exactly one of the digits as 6.

#### How many numbers are there between 100 and 1000 such that exactly one of their digits is 3 if repetition?

Clearly, the numbers between 100 and 1000 are 3-digit numbers. So, we have to form 3-digit numbers such that at least one of their digits is 7. Case I Three -digit numbers with 7 at unit’s place: The number of ways to fill the hundred’s place =9 [by any digit from 1 to 9].

**How many numbers are there between 100 and 1000 which have exactly one of their digits as 8?**

So, it can be filled in 9 different ways. The hundreds place can have any one of the digits except 0 and 7. So, it can be filled in 8 different ways. Therefore, there are 9 x 8 = 72 such numbers.

**How many numbers between 1 to 100 are both squares and cubes?**

Answer: 1 and 64 are only numbers from 1 to 100 that are both perfect squares and cubes.

## How many numbers are there between 1 and 1000?

Hence, there are total 143 numbers between 1 and 1000 which when divided by 7 leave remainder 4.

### How many numbers are there between 100 and 999?

Hence there are 320 such numbers between 100 and 999 which are odd and have distinct digits. Note: Students should note that at hundreds place zero cannot be placed as no three digit number starts with zero and hence it can be filled by only 8 ways.

#### How many numbers from 1 to 1000 are perfect squares and cubes?

There are 1000 integers from 1 to 1000. In these 1000 numbers, There are 31 perfect squares ( from 1² to 31²= 961 , 32² =1024 > 1000). And only 10 perfect cubes ( from 1³ to 10³ = 1000). And 3 numbers are both cube and square numbers.

**How many numbers from 1 to 100 are perfect squares or perfect cubes?**

1 and 64 are only numbers from 1 to 100 that are both perfect squares and cubes.

**How many zeros are there from 1 to 1000?**

192 zeroes if 1000 is counted.

## How many numbers from 1 to 100 are there?

There are 98 whole numbers between 1 and 100.

### What is the number of 3 digit numbers from 100 to 999?

121 numbers

60 + 36 + 16 + 9 = 121 numbers. Hence, three digit numbers from 100 to 999 including all the numbers which have any one digit that is the average of the other two are 121.

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