Table of Contents

- 1 How many threes are there from 1 to 1000?
- 2 How many times does the 3 occur between 1 and 100?
- 3 How many times does the digit 5 appears from 1 to 1000?
- 4 How many times does the digit 5 appear from 1 to 1000?
- 5 How many integers from 100 to 10000 have exactly 3 digits that are the same?
- 6 How many times does the digit 7 appears from 1 to 1000?
- 7 How many numbers between 1 and 1000 contain the digit 0?
- 8 How many times can 3 go into 1000?
- 9 How many numbers are between 1 and 1000 without a 3?
- 10 How many times is the number 3 written thrice?

## How many threes are there from 1 to 1000?

Interview Answers 9^3 = 729 permutations of a base 9 numbering system (a system with no number 3) with 3 digits, since 10^3 = 1000; 10^3 – 9^3 = 271 thus 271 numbers have a 3 in them. 1000 does not contain a 3. So, count the number of 3 digit numbers without a three.

## How many times does the 3 occur between 1 and 100?

Clearly, from 1 to 100, there are ten numbers with 3 as the unit’s digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten’s digit – 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. So, required number = 10 + 10 = 20.

**How many times does the digit 3 occur in the hundreds place in the number between 100 and 1000?**

For numbers between 100 to 1000 , 3 is present in the hundreds place from 300 to 399 (100 times).

### How many times does the digit 5 appears from 1 to 1000?

Hence, the digit 5 appears 300 times from 1 to 1000.

### How many times does the digit 5 appear from 1 to 1000?

**How many times does the digit 3 occur at tens place in natural numbers from 100 to 1000?**

Answer: 3 occurs 90 times in tens and 90 times in the unit place in the numbers from 100 to 1000.

## How many integers from 100 to 10000 have exactly 3 digits that are the same?

This gives 288 ways. There are 9 ways to choose a nonzero repeated digit with 0 for the other. The 0 can go in only three places, so this is 27 ways.

## How many times does the digit 7 appears from 1 to 1000?

7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9. You have 1 × 9 × 9 = 81 such numbers.

**How many times will the digit 5 appear between 1 and 1000?**

### How many numbers between 1 and 1000 contain the digit 0?

The digit zero appears only in the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Thus, there are 11 zeros among the digits. This is the same as the number of digits in writing the numbers from 1 to 10. Now let us look at the numbers from 1 to 1000.

### How many times can 3 go into 1000?

How many times can 3 go into 1000? To find the number of times that 3 goes into 1000, we divide 1000 by 3 to get 333, with a remainder of 1. We have to ignore this remainder, as it is below 3. This means that 3 goes into 1000: 333 times.

**How many times does 3 appear in a number?**

There will be 9 such numbers. However, this digit which is not 3 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers. In each of these 27 numbers, the digit 3 is written twice. Therefore, 3 is written 54 times.

## How many numbers are between 1 and 1000 without a 3?

So, there are 729 numbers without a 3, and 1000-729 = 271 with a 3. I have a much simpler and faster method: let A be the cardinality of numbers between 1 and 1000 that contain a 3 and let A’ be the cardinality of numbers between 1 and 1000 that do not contain a 3.

## How many times is the number 3 written thrice?

The number in which 3 appears thrice – 333 – 1 number. 3 is written thrice in it. Therefore, the total number of times the digit 3 is written between 1 and 999 is 243 + 54 + 3 = 300